Research article Special Issues

New Hermite-Hadamard inequalities in fuzzy-interval fractional calculus via exponentially convex fuzzy interval-valued function

  • Received: 13 June 2021 Accepted: 29 July 2021 Published: 26 August 2021
  • MSC : 26A51

  • In the present note, we develop Hermite-Hadamard type inequality and He's inequality for exponential type convex fuzzy interval-valued functions via fuzzy Riemann-Liouville fractional integral and fuzzy He's fractional integral. Moreover, we establish Hermite-Fejér inequality via fuzzy Riemann-Liouville fractional integral.

    Citation: Yanping Yang, Muhammad Shoaib Saleem, Waqas Nazeer, Ahsan Fareed Shah. New Hermite-Hadamard inequalities in fuzzy-interval fractional calculus via exponentially convex fuzzy interval-valued function[J]. AIMS Mathematics, 2021, 6(11): 12260-12278. doi: 10.3934/math.2021710

    Related Papers:

  • In the present note, we develop Hermite-Hadamard type inequality and He's inequality for exponential type convex fuzzy interval-valued functions via fuzzy Riemann-Liouville fractional integral and fuzzy He's fractional integral. Moreover, we establish Hermite-Fejér inequality via fuzzy Riemann-Liouville fractional integral.



    加载中


    [1] J. Hadamard, Etude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
    [2] C. Hermite, Sur deux limites d'une intégrale définie, Mathesis, 3 (1883), 82.
    [3] M. Z. Sarikaya, E. Set, H. Yaldiz, N. Başak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modell., 57 (2013), 2403-2407.
    [4] M. Kadakal, İ. İşcan, Exponential type convexity and some related inequalities, J. Inequal. Appl., 2020 (2020), 82. doi: 10.1186/s13660-020-02349-1
    [5] D. F. Zhao, T. Q. An, G. J. Ye, W. Liu, New Jensen and Hermite-Hadamard type inequalities for $h$-convex interval-valued functions, J. Inequal. Appl., 2018 (2018), 302.
    [6] H. Budak, T. Tunş, M. Z. Sarikaya, Fractional Hermite-Hadamard-type inequalities for interval-valued functions, Proc. Am. Math. Soc., 148 (2019), 705-718.
    [7] T. Allahviranloo, S. Salahshour, S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Comput., 16 (2012), 297-302.
    [8] S. Wang, H. Zhang, W. W. Zhang, H. M. Zhang, Finite-time projective synchronization of Caputo type fractional complex-valued delayed neural networks, Mathematics, 9 (2021), 1406.
    [9] W. W. Zhang, H. Zhang, J. D. Cao, H. M. Zhang, D. Y. Chen, Synchronization of delayed fractional-order complex-valued neural networks with leakage delay, Phys. A: Stat. Mech. Appl., 556 (2020), 124710.
    [10] R. Y. Ye, X. H. Liu, H. Zhang, J. D. Cao, Global Mittag-Leffler synchronization for fractional-order BAM neural networks with impulses and multiple variable delays via delayed-feedback control strategy, Neural Proc. Lett., 49 (2019), 1-18.
    [11] W. W. Zhang, H. Zhang, J. D. Cao, F. E. Alsaadi, D. Y. Chen, Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays, Neural Networks, 110 (2019), 186-198.
    [12] H. Zhang, M. L. Ye, R. Y. Ye, J. D. Cao, Synchronization stability of Riemann-Liouville fractional delay-coupled complex neural networks, Phys. A: Stat. Mech. Appl., 508 (2018), 155-165.
    [13] A. Ekinci, M. E. Özdemir, Some new integral inequalities via Riemann-Liouville integral operators, Appl. Comput. Math., 3 (2019), 288-295.
    [14] M. Gürbüz, M. E. Özdemir, On some inequalities for product of different kinds of convex functions, Turk. J. Sci., 5 (2020), 23-27.
    [15] E. Set, A. O. Akdemir, F. Özata, Grüss type inequalities for fractional integral operator involving the extended generalized Mittag-Leffler function, Appl. Comput. Math., 19 (2020), 402-414.
    [16] M. U. Awan, M. A. Noor, K. I. Noor, Some integral inequalities via $\phi_{\lambda}\eta$-preinvex functions, Turkish J. Ineq., 1 (2017), 38-45.
    [17] S. I. Butt, M. Nadeem, G. Farid, On Caputo fractional derivatives via exponential s-convex functions, Turk. J. Sci., 5 (2020), 140-146.
    [18] T. M. Costa, H. Román-Flores, Some integral inequalities for fuzzy-interval-valued functions, Inform. Sci., 420 (2017), 110-125. doi: 10.1016/j.ins.2017.08.055
    [19] O. Kaleva, On fuzzy differential equations, Fuzzy Sets Syst., 24 (1987), 301-317. doi: 10.1016/0165-0114(87)90029-7
    [20] P. O. Mohammed, On new trapezoid type inequalities for h-convex functions via generalized fractional integral, Turk. J. Anal. Number Theory, 6 (2018), 125-128. doi: 10.12691/tjant-6-4-5
    [21] M. B. Khan, P. O. Mohammed, M. A. Noor, Y. S. Hamed, New Hermite-Hadamard inequalities in fuzzy interval fractional calculus and related inequalities, Symmetry, 13 (2021), 673. doi: 10.3390/sym13040673
    [22] P. O. Mohammed, T. Abdeljawad, D. Baleanu, A. Kashuri, F. Hamasalh, P. Agarwal, New fractional inequalities of Hermite-Hadamard type involving the incomplete gamma functions, J. Inequal. Appl., 2020 (2020), 263. doi: 10.1186/s13660-020-02538-y
    [23] J. H. He, A tutorial review on fractal spacetime and fractional calculus, Int. J. Theor. Phys., 53 (2014), 3698-3718. doi: 10.1007/s10773-014-2123-8
    [24] J. H. He, A short remark on fractional variational iteration method, Phys. Lett. A, 375 (2011), 3362-3364. doi: 10.1016/j.physleta.2011.07.033
    [25] J. H. He, A symptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012 (2012), 916793.
    [26] J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20 (2006), 1141-1199. doi: 10.1142/S0217979206033796
    [27] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Amsterdam: Elsevier, 2006.
    [28] B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets Syst., 151 (2005), 581-599. doi: 10.1016/j.fss.2004.08.001
    [29] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst., 161 (2010), 1564-1584. doi: 10.1016/j.fss.2009.06.009
    [30] S. Nanda, K. Kar, Convex fuzzy mappings, Fuzzy Sets Syst., 48 (1992), 129-132. doi: 10.1016/0165-0114(92)90256-4
    [31] R. Goetschel Jr., W. Voxman, Elementary fuzzy calculus, Fuzzy Sets Syst., 18 (1986), 31-43. doi: 10.1016/0165-0114(86)90026-6
    [32] D. Phil, P. Kloeden, Metric spaces of fuzzy sets: Theory and applications, World Scientific: Singapore, 1994.
    [33] B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst., 230 2013,119-141.
    [34] R. P. Agarwal, D. Baleanu, J. J. Nieto, D. F. M. Torres, Y. Zhou, A survey on fuzzy fractional differential and optimal control nonlocal evolution equations, J. Comput. Appl. Math., 339 (2018), 3-29. doi: 10.1016/j.cam.2017.09.039
    [35] D. Zhang, C. Guo, D. Chen, G. Wang, Jensen's inequalities for set-valued and fuzzy set-valued functions, Fuzzy Sets Syst., 2020 (2020), 1-27.
    [36] T. M. Costa, H. Román-Flores, Some integral inequalities for fuzzy-interval-valued functions, Inform. Sci., 420 (2017), 110-125. doi: 10.1016/j.ins.2017.08.055
    [37] T. M. Costa, Jensen's inequality type integral for fuzzy-interval-valued functions, Fuzzy Sets Syst., 327 (2017), 31-47. doi: 10.1016/j.fss.2017.02.001
    [38] R. E. Moore, Interval analysis, Englewood Cliffs: Prentice Hall, USA, 1966.
  • 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(1828) PDF downloads(111) Cited by(2)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog