Research article Special Issues

Beyond the implications of Grand Ethiopian Renaissance Dam filling policies

  • The Grand Ethiopian Renaissance Dam (GERD) in Ethiopia and High Aswan Dam (HAD) in Egypt both operate on the Nile River, independent of a governing international treaty or agreement. As a result, the construction of the GERD, the Earth's eighth largest dam, ignited a furious debate among Ethiopia, Sudan, and Egypt on its filling policies and long-term operation. Ethiopia and Egypt's stance on the Nile River's water resources, combined with a nationalistic policy debate on the GERD's filling policies and long-term operation, has severely affected progress toward reaching agreeable terms before the first round of GERD filling was completed. These three countries continue to debate on the terms of agreement for the second round of GERD filling, scheduled to start by July 2021. We examined the GERD filling strategy for five- and six-year terms using time series data for the periods 1979–1987 and 1987–1992 to combine analyses for dry and wet seasons and investigate the potential impacts of filling the GERD above the downstream HAD using four HAD starting water levels. A model calibrated using MIKE Hydro results shows that during both five- and six-year terms of future GERD filling, Egypt would not need to invoke the HAD's minimum operating level. We pursued a narrative approach that appeals to both a technical and non-technical readership, and our results show the urgent need for cooperation at both policy and technical levels to mitigate and adapt to future climate change through the development of climate-proof agreements. Moreover, the results call for the riparian countries to move away from the current nationalistic policy debate approach and pursue a more cooperative, economically beneficial, and climate adaptive approach.

    Citation: Abay Yimere, Engdawork Assefa. Beyond the implications of Grand Ethiopian Renaissance Dam filling policies[J]. AIMS Geosciences, 2021, 7(3): 313-330. doi: 10.3934/geosci.2021019

    Related Papers:

    [1] Chunyan Luo, Yuping Yu, Tingsong Du . Estimates of bounds on the weighted Simpson type inequality and their applications. AIMS Mathematics, 2020, 5(5): 4644-4661. doi: 10.3934/math.2020298
    [2] Sabir Hussain, Javairiya Khalid, Yu Ming Chu . Some generalized fractional integral Simpson’s type inequalities with applications. AIMS Mathematics, 2020, 5(6): 5859-5883. doi: 10.3934/math.2020375
    [3] Muhammad Tariq, Hijaz Ahmad, Soubhagya Kumar Sahoo, Artion Kashuri, Taher A. Nofal, Ching-Hsien Hsu . Inequalities of Simpson-Mercer-type including Atangana-Baleanu fractional operators and their applications. AIMS Mathematics, 2022, 7(8): 15159-15181. doi: 10.3934/math.2022831
    [4] Xuexiao You, Fatih Hezenci, Hüseyin Budak, Hasan Kara . New Simpson type inequalities for twice differentiable functions via generalized fractional integrals. AIMS Mathematics, 2022, 7(3): 3959-3971. doi: 10.3934/math.2022218
    [5] Maimoona Karim, Aliya Fahmi, Shahid Qaisar, Zafar Ullah, Ather Qayyum . New developments in fractional integral inequalities via convexity with applications. AIMS Mathematics, 2023, 8(7): 15950-15968. doi: 10.3934/math.2023814
    [6] Saad Ihsan Butt, Artion Kashuri, Muhammad Umar, Adnan Aslam, Wei Gao . Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals. AIMS Mathematics, 2020, 5(5): 5193-5220. doi: 10.3934/math.2020334
    [7] Areej A. Almoneef, Abd-Allah Hyder, Fatih Hezenci, Hüseyin Budak . Simpson-type inequalities by means of tempered fractional integrals. AIMS Mathematics, 2023, 8(12): 29411-29423. doi: 10.3934/math.20231505
    [8] Naila Mehreen, Matloob Anwar . Some inequalities via Ψ-Riemann-Liouville fractional integrals. AIMS Mathematics, 2019, 4(5): 1403-1415. doi: 10.3934/math.2019.5.1403
    [9] Ghulam Farid, Saira Bano Akbar, Shafiq Ur Rehman, Josip Pečarić . Boundedness of fractional integral operators containing Mittag-Leffler functions via (s,m)-convexity. AIMS Mathematics, 2020, 5(2): 966-978. doi: 10.3934/math.2020067
    [10] Yousaf Khurshid, Muhammad Adil Khan, Yu-Ming Chu . Conformable fractional integral inequalities for GG- and GA-convex functions. AIMS Mathematics, 2020, 5(5): 5012-5030. doi: 10.3934/math.2020322
  • The Grand Ethiopian Renaissance Dam (GERD) in Ethiopia and High Aswan Dam (HAD) in Egypt both operate on the Nile River, independent of a governing international treaty or agreement. As a result, the construction of the GERD, the Earth's eighth largest dam, ignited a furious debate among Ethiopia, Sudan, and Egypt on its filling policies and long-term operation. Ethiopia and Egypt's stance on the Nile River's water resources, combined with a nationalistic policy debate on the GERD's filling policies and long-term operation, has severely affected progress toward reaching agreeable terms before the first round of GERD filling was completed. These three countries continue to debate on the terms of agreement for the second round of GERD filling, scheduled to start by July 2021. We examined the GERD filling strategy for five- and six-year terms using time series data for the periods 1979–1987 and 1987–1992 to combine analyses for dry and wet seasons and investigate the potential impacts of filling the GERD above the downstream HAD using four HAD starting water levels. A model calibrated using MIKE Hydro results shows that during both five- and six-year terms of future GERD filling, Egypt would not need to invoke the HAD's minimum operating level. We pursued a narrative approach that appeals to both a technical and non-technical readership, and our results show the urgent need for cooperation at both policy and technical levels to mitigate and adapt to future climate change through the development of climate-proof agreements. Moreover, the results call for the riparian countries to move away from the current nationalistic policy debate approach and pursue a more cooperative, economically beneficial, and climate adaptive approach.



    Critical materials are garnering many research interests from academia, industry, and defense sectors due to their increasing demand for clean-energy solutions and the potential for significant supply risks. These materials include cobalt, lithium, manganese, and rare earth elements (REEs), which have limited production capacities but are increasingly used in lithium-ion batteries (LIBs) and neodymium–iron–boron (Nd–Fe–B) magnets for electric vehicles (EVs), and renewable energy generation and/or storage. To achieve net zero emissions by 2050, the demand for these critical materials is projected to surpass the supply. Increased mining of critical materials from ores creates extra burdens or disturbances on the environment and affected communities, and recycling of these valuable materials from end-of-life (EOL) products can be a promising alternative from both economic and environmental perspectives. This special issue aims to gather up-to-date knowledge related to cutting-edge research in the broad scientific area of critical materials for clean energy applications.

    This special issue consists of five articles. In the first paper of this special issue, Alipanah et al. [1] presented a review of emerging technologies and pathways such as refurbishing, direct recycling (i.e., cathode-to-cathode), and hydrometallurgical and pyrometallurgical processes for critical materials recovery from spent LIBs. The study revealed the economic and environmental advantages of LIB reuse over materials recycling, though significant research and infrastructure developments are required. Among the materials recycling methods, direct recycling is superior in closing the loop with less chemicals and energy consumed. However, high operational costs and changes in battery chemistry over time could limit the widespread application of direct recycling. To this end, this paper also reviewed the government policies adopted by Europe and the US for promoting LIB recycling.

    In the second review paper, Ji et al. [2] provided a comprehensive review on the recent advancements in each step of the direct recycling process, namely, harvesting cathode materials, separation of cathode active materials from other components through thermal and floatation processes, and regeneration of degraded electrochemical performance of homogenous cathode materials through relithiation (e.g., solid-state relithiation, hydrothermal relithiation). The authors emphasized complete separation of cathode materials from binders and carbon, as the presence of residue affected the electrochemical performance of regenerated cathode materials. Moreover, they suggested future endeavors to minimize fluoride emissions during the separation process.

    The special issue includes another mini-review paper on recent advances in acid-free dissolution and separation of REEs from Nd–Fe–B and samarium–cobalt (Sm–Co) magnet wastes by Inman et al. [3]. The research was motivated by the fact that acid-based hydrometallurgical processes generate substantial amounts of hazardous waste, which needs to be controlled to avoid environmental hazards for recovering REEs. A promising solution is to dissolve magnet materials using an aqueous solution of a copper (Ⅱ) salt, which transfers pertinent REEs to the dissolved solution. With further filtration, precipitation, and calcination procedures, mixed rare earth oxides were produced with a yield of > 98%. Separation of heavy REEs (e.g., Dy) from light REEs (e.g., Nd, Pr) was also investigated, highlighting the research need to develop economically and environmentally sound alternatives to traditional solvent extraction (SX) route.

    Alongside these review papers, the special issue includes two research articles. In the first article, Maria et al. [4] emphasized the inclusion of temporal information while calculating the environmental impacts of buildings. The authors performed life cycle analysis to evaluate both static and dynamic global warming impact for two newly developed construction materials: (ⅰ) goethite-based inorganic polymers (GIP), and (ⅱ) stainless steel slag-based alkali-activated aerated blocks (SSSaer), compared to traditional autoclaved aerated ordinary Portland cement (OPC) concrete. Although both static and dynamic approaches provided similar results, the latter allowed a more informed analysis of emission flows over time. According to their analysis, GIP presents the highest global warming impact at any time horizon, both for the static and the dynamic approach, while SSSaer has the lowest impact.

    As the final article of the special issue, Nguyen et al. [5] presented a market-oriented critical-materials database, which aimed to help material researchers gain a better understanding of the market for 29 critical materials. The database provided insightful information regarding the most impactful applications of each element, as well as their industry specifications, prices, product composition, and global consumption.

    We would like to thank all the authors and reviewers who have contributed their exceptional work to this special issue of Critical Materials for Low Carbon Society. We also appreciate the technical and administrative support from the editors and editorial board members of the Journal of Clean Technologies and Recycling. We hope this special issue provides an archive of stimulating articles that contribute to industrial decarbonization.

    The authors have no conflicts of interest to declare.



    [1] Nile Basin Initiative (2016) Nile Basin Water Resources Atlas. Entebbe, Uganda: NBI.
    [2] United States Bureau of Reclamation (1964) Land and Water Resources of the Blue Nile Basin, Main Report. United States Department of Interior Bureau of Reclamation, Washington, DC, USA.
    [3] Nile Basin Initiative (2012) State of the River Nile Basin 2012. Nile Basin Initiative, Entebbe.
    [4] Nile Basin Initiative (2014) Nile Basin decision support system DSS: Modeling tools training module. Entebbe
    [5] Wheeler KG, Jeuland M, Hall JW, et al. (2020) Understanding and managing new risks on the Nile with the Grand Ethiopian Renaissance Dam. Nat Commun 11: 5222. doi: 10.1038/s41467-020-19089-x
    [6] Ministry of Finance and Economic Development (2010) Growth and Transformation Plan 2010/11-2014/15. Addis Ababa.
    [7] Allan A (1999) The Nile Basin: Evolving Approaches to Nile Waters Management SOAS Water Issues Group, Occasional Paper 20 June. University of London, UK. Available from: https://www.soas.ac.uk/water/publications/papers/file38363.pdf.
    [8] Waterbury J (2002) The Nile Basin: National Determinants of Collective Action, Yale University Press, New Haven, Connecticut.
    [9] Arsano Y (2007) Ethiopia and the Nile: Dilemmas of National and Regional Hydropolitics. Swiss Federal Institute of Technology, Zurich, 324
    [10] World Bank (1997) Introduction to environmental and social assessment requirements and procedures for World Bank-financed projects. Available from: http://documents1.worldbank.org/curated/en/479901468174250106/pdf/multi0page.pdf.
    [11] Whittington D, Waterbury J, Jeuland M (2014) The Grand Renaissance Dam and prospects for cooperation on the Eastern Nile. Water Policy 16: 595-608. doi: 10.2166/wp.2014.011b
    [12] Block PJ, Strzepek K (2010) Economic analysis of large-scale upstream river basin development on the Blue Nile in Ethiopia considering transient conditions, climate variability, and climate change. J Water Resour Plan Manag 136: 156-166 doi: 10.1061/(ASCE)WR.1943-5452.0000022
    [13] McCartney MP, Girma MM (2012) Evaluating the downstream implications of planned water resource development in the Ethiopian portion of the Blue Nile River. Water Int 37: 362-379. doi: 10.1080/02508060.2012.706384
    [14] Arjoon D, Mohamed Y, Goor Q, et al. (2014) Hydro-economic risk assessment in the eastern Nile River basin. Water Resour Econ 8: 16-31 doi: 10.1016/j.wre.2014.10.004
    [15] Bates A, Tuncok K, Barbour T, et al. (2013) First joint multipurpose program identification: Strategic perspectives and options assessment on the Blue Nile multipurpose development- Working Paper 2. Addis Ababa: Author Report to Nile Basin Initiative.
    [16] International Panel of Experts (2013) Grand Ethiopian Renaissance Dam: Project final report. Addis Ababa, Ethiopia
    [17] King A, Block P (2014) An assessment of reservoir filling policies for the Grand Ethiopian Renaissance Dam. J Water Clim Change 5: 233-243. doi: 10.2166/wcc.2014.043
    [18] Mulat AG, Moges SA (2014) Assessment of the impact of the Grand Ethiopian Renaissance Dam on the performance of the High Aswan Dam. J Water Resour Prot 6: 583-598. doi: 10.4236/jwarp.2014.66057
    [19] Ahmed AT, Elsanabary MH (2015) Hydrological and environmental impacts of Grand Ethiopian Renaissance Dam on the Nile river. In: Proceedings of the Eighteenth International Water Technology Conference, IWTC18, Sharm El Sheikh, Egypt, 12-14.
    [20] Zhang Y, Block P, Hammond M, et al. (2015) Ethiopia's Grand Renaissance Dam: Implications for downstream riparian countries. J Water Resour Plann Manage 141: 05015002. doi: 10.1061/(ASCE)WR.1943-5452.0000520
    [21] Soliman G, Soussa H, El-Sayed S (2016) Assessment of Grand Ethiopian Renaissance Dam impacts using decision support system. IOSR J Comput Eng 18: 8-18.
    [22] Wheeler KG, Basheer M, Mekonnen ZT, et al. (2016) Cooperative filling approaches for the Grand Ethiopian Renaissance Dam. Water Int 41: 611-634. doi: 10.1080/02508060.2016.1177698
    [23] Liersch S, Koch H, Hattermann F, et al. (2017) Management scenarios of the Grand Ethiopian Renaissance Dam and their impacts under recent and future climates. Water 9: 728. doi: 10.3390/w9100728
    [24] Mohamed HI (2017) Grand Ethiopian Renaissance Dam impact on long term operation of high Aswan Dam reservoir. Int J Water Resour Arid Environ 6: 89-95.
    [25] Block P, Strzepek K (2012) Power Ahead: Meeting Ethiopia's Energy Needs Under a Changing Climate. Rev Dev Econ 16: 476-488. doi: 10.1111/j.1467-9361.2012.00675.x
    [26] Jeuland M, Whittington D (2014) Water resources planning under climate change: assessing the robustness of real options for the Blue Nile. Water Resour Res 50: 2086-2107 doi: 10.1002/2013WR013705
    [27] Siam MS, Eltahir EAB (2017) Climate change enhances interannual variability of the Nile river flow. Nat. Clim Change 7: 350-354
    [28] Conway D (2017) Water resources: future Nile river flows. Nat Clim Change 7: 319-320 doi: 10.1038/nclimate3285
    [29] Turkmen N, Aslan M, Duzenli A (2005) Floristic characters of the Karkamıs Dam reservoir area and its surroundings (Gaziantep-Sanliurfa: Turkey). Biodiversity Conserv 14: 2291-2297. doi: 10.1007/s10531-004-1664-1
    [30] Hopkins SN, Mehanna RS (2010) Nubian Encounters: The Story of the Nubian Ethnological Survey 1961-1964, The American University in Cairo Press, Cairo.
    [31] Goubachi Y (2012) Impact of lake Nasser on the groundwater of the Nubia sandstone aquifer system in Tushka area, South Western Desert, Egypt. J King Saud Univ Sci 24: 101-109. doi: 10.1016/j.jksus.2010.04.005
    [32] Akça E, Fujikura R, Sabbağ Ç (2013) Atatürk Dam resettlement process: increased disparity resulting from insufficient financial compensation. Int J Water Resour Dev 29: 101-108. doi: 10.1080/07900627.2012.738497
    [33] Kleinitz C, Naser C (2013) The loss of innocence: political and ethical dimensions of the Merowe dam archaeological salvage project at the fourth Nile cataract (Sudan). Conserv Manage Archaeol Sites 13: 253-280. doi: 10.1179/175355211X13179154166231
    [34] Marchetti N, Curci A, Gatto MC, et al. (2019) A Multi-scalar Approach for Assessing the Impact of Dams on the Cultural Heritage in the Middle East and Northern Africa. J Cult Heritage 37: 17-28. doi: 10.1016/j.culher.2018.10.007
    [35] Marchetti N, Bitelli G, Franci F, et al. (2020) Archaeology and Dams in South-eastern Turkey: Post-Flooding Damage Assessment and Safeguarding Strategies on Cultural Heritage. J Mediterr Archaeol 33: 29-54. doi: 10.1558/jma.42345
    [36] Conway D, Hulme M (1993) Recent fluctuations in precipitation and runoff over the Nile sub-basins and their impact on main Nile discharge. Clim Change 25: 127-151. doi: 10.1007/BF01661202
    [37] Conway D (2000) The climate and hydrology of the Upper Blue Nile River. Geogr J 166: 49-62. doi: 10.1111/j.1475-4959.2000.tb00006.x
    [38] Shahin M (1985) Hydrology of the Nile Basin. Elsevier, Amsterdam, 575.
    [39] Sutcliffe P (1999) The Hydrology of the Nile, IAHS Special Publication No. 5. IAHS Press, Institute of Hydrology, Wallingford, Oxford shire OX10 8BB, UK. Available from: http://www.hydrosciences.fr/sierem/produits/biblio/hydrology%20of%20.
    [40] Shahin M (2002) Hydrology and Water Resources of Africa, Water Science and Technology Library. Kluwer Academic Publishers, Dordrecht/Boston/London.
    [41] Whittington D, Wu X, Sadoff C (2005) Water resources management in the Nile basin: The economic value of cooperation. Water Policy 7.
    [42] MacChesney B (1959) Lake Lanoux case (France-Spain). Am J Int Law 53: 156-171. doi: 10.2307/2195225
    [43] Payne CR (2011) Pulp Mills on the River Uruguay (Argentina v. Uruguay). Am J Int Law 105: 94-101.
    [44] Abbay Basin Atlas (2015) Abbay Bain Authority, Bahir Dar Office, Ethiopia.
    [45] Awulachew SB, Yilma AD, Loulseged M, et al. (2007) Water resources and irrigation development in Ethiopia. Iwmi 123.
    [46] Diro GT, Grimes DIF, Black E (2011) Teleconnections between Ethiopian summer rainfall and sea surface temperature: Part I—Observation and modelling. Clim Dyn 37: 103-119. doi: 10.1007/s00382-010-0837-8
    [47] Swain A (2002) The Nile River Basin initiative: Too many cooks, too little broth. SAIS Rev 22: 293-308 doi: 10.1353/sais.2002.0044
    [48] Tvedt T (2004) The river Nile in the age of the British: Political ecology and the quest for economic power. London: I.B.Tauris & Co. Ltd.
    [49] Blackmore D, Whittington D (2008) Opportunities for cooperative water resources development on the Eastern Nile: Risks and rewards. An independent report of the scoping study team to the Eastern Nile Council of Ministers. Available from: https://planning.unc.edu/people/faculty/dalewhittington/BlackmoreWhittingtonENScopingStudyFinal2009.pdf.
    [50] Yao H, Georgakakos AP (2003) The Nile Decision Support Tool, River Simulation and Management (Report No. GCP/INT/752/ITA). Georgia Institute of Technology, Atlanta.
    [51] Jonker V, Beuster H, Sparks A, et al. (2012) Data Compilation and Pilot Application of the Nile Basin Decision Support System (NB-DSS): Scenario Analysis Report: Work package 2: Stage 2 Scenario Analysis Report: Integrated Nile Basin (Report No. 7327/107486). Cape Town: Author Report to Nile Basin Initiative.
    [52] Eastern Nile Technical Regional Office (ENTRO) (2015) Coordinated Investment Planning—Generation. Eastern Nile Power Trade Program Study. African Development Bank, Abidjan, Ivory Coast.
    [53] Kahsay TN, Kuik O, Brouwer R, et al. (2015) Estimation of the transboundary economic impacts of the Grand Ethiopia Renaissance Dam: A computable general equilibrium analysis. Water Resour Econ 10: 14-30. doi: 10.1016/j.wre.2015.02.003
    [54] Hurst H. E, Black RP, Simaika YM (1965) Long-term storage: an experimental study. (Constable).
    [55] Taye MT, Willems P, Block P (2015) Implications of climate change on hydrological extremes in the Blue Nile basin: a review. J Hydrol Regional Stud 4: 280-293. doi: 10.1016/j.ejrh.2015.07.001
    [56] Denning S (2006) Effective storytelling: strategic business narrative techniques. Strategy Leadersh 34: 42-48. doi: 10.1108/10878570610637885
    [57] Digna RF, Mohamed AY, Van der Zaag P, et al. (2018) Impact of water resources development on water availability for hydropower production and irrigated agriculture of the Eastern Nile Basin. J. Water Resour. Plan Manag 144: 05018007.
    [58] Cervigni Aello R, Liden R, Neumann JE, et al. (2015) Enhancing the Climate Resilience of Africa's Infrastructure: The Power and Water Sectors. World Bank, Washington, DC.
    [59] Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica. Econometric Soc 47: 263-291
    [60] Kahneman D, Slovic P, Tversky A (1982) Judgment Under Uncertainty: Heuristics and Biases, Cambridge University Press, Cambridge, UK.
    [61] Kahneman D (2013) Thinking, Fast and Slow, Farrar, Straus & Giroux, New York.
    [62] Kahneman D, Sibony D, Sunstein C R (2021) Noise: A Flaw in Human Judgment, New York, Little Brown Spark, 464.
    [63] Kahneman D, Rosenfield M. A, Gandhi L, et al. (2018) Noise: How to Overcome the High, Hidden Cost of Inconsistent Decision Making. Harvard Business Review (HBR). P 38-52. Available from: https://hbsp.harvard.edu/product/10137-PDF-ENG?Ntt=%20Harvard%20Business%20Review%202018%20Ten%20most%20reads%20.
    [64] Veilleux J (2013) The Human Security Dimensions of Dam Development: The Grand Ethiopian Renaissance Dam. Global Dialogue 15.
    [65] Tversky A, Kahneman D (1981) The framing of decisions and the psychology of choice. Science 211: 453-458. doi: 10.1126/science.7455683
    [66] Sibony O (2019) You Are About to Make A Terrible Mistake! How Biases Distort Decision Making- and What You Can DO to Fight Them, Little Brown Spark, New York, 356.
    [67] Griffiths JG (1966) Hecataeus and Herodotus on "A Gift of the River". J Near East Stud 25: 57-61. doi: 10.1086/371846
    [68] Whittington, D (2016) Policy note: ancient instincts—implications for water policy in the 21st century. Water Econ Policy 2: 1671002. doi: 10.1142/S2382624X16710028
    [69] Julien F (2012) Hydropolitics is what societies make of it (or why we need a constructivist approach to the geopolitics of water). Int J Sustainable Soc 4: 45-71. doi: 10.1504/IJSSOC.2012.044665
    [70] Moravcsik A (1997) Taking preferences seriously: A liberal theory of international politics. Int Organ 51: 513-553. doi: 10.1162/002081897550447
    [71] Jaya Ramji-Nogales, Andrew IS, Schrag G, et al. (2007) Refugee Roulette: Disparities in Asylum Adjudication. Stanford Law Review. Available from: https://scholarship.law.georgetown.edu/facpub/1902https://ssrn.com/abstract=983946.
  • This article has been cited by:

    1. Saima Rashid, Muhammad Aslam Noor, Khalida Inayat Noor, Farhat Safdar, Yu-Ming Chu, Hermite-Hadamard Type Inequalities for the Class of Convex Functions on Time Scale, 2019, 7, 2227-7390, 956, 10.3390/math7100956
    2. Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira Kalsoom, Yu-Ming Chu, Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function, 2019, 7, 2227-7390, 1225, 10.3390/math7121225
    3. Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Grüss-type integrals inequalities via generalized proportional fractional operators, 2020, 114, 1578-7303, 10.1007/s13398-020-00823-5
    4. Muhammad Samraiz, Fakhra Nawaz, Sajid Iqbal, Thabet Abdeljawad, Gauhar Rahman, Kottakkaran Sooppy Nisar, Certain mean-type fractional integral inequalities via different convexities with applications, 2020, 2020, 1029-242X, 10.1186/s13660-020-02474-x
    5. Thabet Abdeljawad, Saima Rashid, Zakia Hammouch, İmdat İşcan, Yu-Ming Chu, Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications, 2020, 2020, 1687-1847, 10.1186/s13662-020-02955-9
    6. Zeynep ŞANLI, SIMPSON TYPE INTEGRAL INEQUALITIES FOR HARMONIC CONVEX FUNCTIONS VIA CONFORMABLE FRACTIONAL INTEGRALS, 2020, 2147-1630, 10.37094/adyujsci.780433
    7. Thabet Abdeljawad, 2020, 9781119654223, 133, 10.1002/9781119654223.ch5
    8. Shuang-Shuang Zhou, Saima Rashid, Saima Parveen, Ahmet Ocak Akdemir, Zakia Hammouch, New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators, 2021, 6, 2473-6988, 4507, 10.3934/math.2021267
    9. Thabet Abdeljawad, Saima Rashid, Zakia Hammouch, Yu-Ming Chu, Some new local fractional inequalities associated with generalized (s,m)-convex functions and applications, 2020, 2020, 1687-1847, 10.1186/s13662-020-02865-w
    10. Humaira Kalsoom, Saima Rashid, Muhammad Idrees, Yu-Ming Chu, Dumitru Baleanu, Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions, 2019, 12, 2073-8994, 51, 10.3390/sym12010051
    11. Saima Rashid, Fahd Jarad, Zakia Hammouch, Some new bounds analogous to generalized proportional fractional integral operator with respect to another function, 2021, 0, 1937-1179, 0, 10.3934/dcdss.2021020
    12. Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Khalida Inayat Noor, Dumitru Baleanu, Jia-Bao Liu, On Grüss inequalities within generalized K-fractional integrals, 2020, 2020, 1687-1847, 10.1186/s13662-020-02644-7
    13. Saad Ihsan Butt, Mehroz Nadeem, Shahid Qaisar, Ahmet Ocak Akdemir, Thabet Abdeljawad, Hermite–Jensen–Mercer type inequalities for conformable integrals and related results, 2020, 2020, 1687-1847, 10.1186/s13662-020-02968-4
    14. Saima Rashid, Muhammad Amer Latif, Zakia Hammouch, Yu-Ming Chu, Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions, 2019, 11, 2073-8994, 1448, 10.3390/sym11121448
    15. SAIMA RASHID, ZAKIA HAMMOUCH, FAHD JARAD, YU-MING CHU, NEW ESTIMATES OF INTEGRAL INEQUALITIES VIA GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION, 2020, 28, 0218-348X, 2040027, 10.1142/S0218348X20400277
    16. Fatih Hezenci, Hüseyin Budak, Hasan Kara, New version of fractional Simpson type inequalities for twice differentiable functions, 2021, 2021, 1687-1847, 10.1186/s13662-021-03615-2
    17. Hüseyin Budak, Seda Kilinç Yildirim, Hasan Kara, Hüseyin Yildirim, On new generalized inequalities with some parameters for coordinated convex functions via generalized fractional integrals, 2021, 44, 0170-4214, 13069, 10.1002/mma.7610
    18. Muhammad Aamir Ali, Hasan Kara, Jessada Tariboon, Suphawat Asawasamrit, Hüseyin Budak, Fatih Hezenci, Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators, 2021, 13, 2073-8994, 2249, 10.3390/sym13122249
    19. Humaira Kalsoom, Hüseyin Budak, Hasan Kara, Muhammad Aamir Ali, Some new parameterized inequalities for co-ordinated convex functions involving generalized fractional integrals, 2021, 19, 2391-5455, 1153, 10.1515/math-2021-0072
    20. İmdat İşcan, Erhan Set, Ahmet Ocak Akdemir, Alper Ekinci, Sinan Aslan, 2023, 9780323909532, 157, 10.1016/B978-0-32-390953-2.00017-7
    21. MIAO-KUN WANG, SAIMA RASHID, YELIZ KARACA, DUMITRU BALEANU, YU-MING CHU, NEW MULTI-FUNCTIONAL APPROACH FOR κTH-ORDER DIFFERENTIABILITY GOVERNED BY FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ℏ)-CONVEX FUNCTIONS IN HILBERT SPACE, 2021, 29, 0218-348X, 2140019, 10.1142/S0218348X21400193
    22. Saima Rashid, Dumitru Baleanu, Yu-Ming Chu, Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems, 2020, 18, 2391-5471, 478, 10.1515/phys-2020-0114
    23. Xuexiao You, Fatih Hezenci, Hüseyin Budak, Hasan Kara, New Simpson type inequalities for twice differentiable functions via generalized fractional integrals, 2022, 7, 2473-6988, 3959, 10.3934/math.2022218
    24. YONG-MIN LI, SAIMA RASHID, ZAKIA HAMMOUCH, DUMITRU BALEANU, YU-MING CHU, NEW NEWTON’S TYPE ESTIMATES PERTAINING TO LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p-CONVEXITY WITH APPLICATIONS, 2021, 29, 0218-348X, 2140018, 10.1142/S0218348X21400181
    25. Miguel Vivas-Cortez, Pshtiwan O. Mohammed, Y. S. Hamed, Artion Kashuri, Jorge E. Hernández, Jorge E. Macías-Díaz, On some generalized Raina-type fractional-order integral operators and related Chebyshev inequalities, 2022, 7, 2473-6988, 10256, 10.3934/math.2022571
    26. Yu-Ming Chu, Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira Kalsoom, More new results on integral inequalities for generalized K-fractional conformable Integral operators, 2021, 14, 1937-1179, 2119, 10.3934/dcdss.2021063
    27. Nassima Nasri, Badreddine Meftah, Abdelkader Moumen, Hicham Saber, Fractional 3/8-Simpson type inequalities for differentiable convex functions, 2024, 9, 2473-6988, 5349, 10.3934/math.2024258
    28. Fatih Hezenci, Hüseyin Budak, A note on fractional Simpson-like type inequalities for functions whose third derivatives are convex, 2023, 37, 0354-5180, 3715, 10.2298/FIL2312715H
    29. Zeynep Sanlı, Simpson type Katugampola fractional integral inequalities via Harmonic convex functions, 2022, 10, 23193786, 364, 10.26637/mjm1004/007
    30. Meriem Merad, Badreddine Meftah, Abdelkader Moumen, Mohamed Bouye, Fractional Maclaurin-Type Inequalities for Multiplicatively Convex Functions, 2023, 7, 2504-3110, 879, 10.3390/fractalfract7120879
    31. Fatih Hezenci, A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions, 2023, 73, 1337-2211, 675, 10.1515/ms-2023-0049
    32. Hüseyin Budak, Fatih Hezenci, Hasan Kara, Mehmet Zeki Sarikaya, Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule, 2023, 11, 2227-7390, 2282, 10.3390/math11102282
    33. Nazakat Nazeer, Ali Akgül, Faeem Ali, Study of the results of Hilbert transformation for some fractional derivatives, 2024, 0228-6203, 1, 10.1080/02286203.2024.2371685
    34. Tarek Chiheb, Badreddine Meftah, Abdelkader Moumen, Mouataz Billah Mesmouli, Mohamed Bouye, Some Simpson-like Inequalities Involving the (s,m)-Preinvexity, 2023, 15, 2073-8994, 2178, 10.3390/sym15122178
    35. Gamzenur Köksaldı, Tuba Tunç, Simpson-type inequalities for the functions with bounded second derivatives involving generalized fractional integrals, 2025, 2025, 1687-2770, 10.1186/s13661-025-02040-8
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(5055) PDF downloads(293) Cited by(2)

Figures and Tables

Figures(8)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog