Search Advanced

AIMS Mathematics

2025, Volume 10, Issue 6: 15025-15039. doi: 10.3934/math.2025674
Previous Article Next Article
Research article

Coupled fixed point results for non-expansive mapping and its applications to the fractional order HIV/AIDS model

  • 1.
    Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • 2.
    Department of Mathematics, Government College, Kabal Swat, Khyber Pakhtunkhwa, Pakistan
  • 3.
    Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
  • 4.
    Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
  • 5.
    Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
  • 6.
    Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
  • Published: 30 June 2025

  • MSC : 47H10, 54H25

  • In this work, we develop certain coupled fixed-point results in Banach space by utilizing the Krasnosel'skii's expansive-type fixed-point results. Additionally, we establish existence and uniqueness conditions for coupled fixed points. Applying these results, we investigate the fractional-order HIV/AIDS model, demonstrating the existence of solutions. Our results contribute to the understanding of complex systems and non linear dynamics.

    Citation: Kamaleldin Abodayeh, Mian Bahadur Zada, Muhammad Sarwar, Haroon Rashid, Saowaluck Chasreechai, Thanin Sitthiwirattham. Coupled fixed point results for non-expansive mapping and its applications to the fractional order HIV/AIDS model[J]. AIMS Mathematics, 2025, 10(6): 15025-15039. doi: 10.3934/math.2025674

    Related Papers:

  • In this work, we develop certain coupled fixed-point results in Banach space by utilizing the Krasnosel'skii's expansive-type fixed-point results. Additionally, we establish existence and uniqueness conditions for coupled fixed points. Applying these results, we investigate the fractional-order HIV/AIDS model, demonstrating the existence of solutions. Our results contribute to the understanding of complex systems and non linear dynamics.



    加载中


    [1] M. Aslam, R. Murtaza, T. Abdeljawad, G. Rahman, A. Khan, H. Khan, et al., A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel, Adv. Difer. Equ., 2021 (2021), 1–15. https://doi.org/10.1186/s13662-021-03264-5 doi: 10.1186/s13662-021-03264-5
    [2] A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and applications to heat transfer model, Thermal Sci., 20 (2016), 763–769. http://dx.doi.org/10.2298/TSCI160111018A doi: 10.2298/TSCI160111018A
    [3] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
    [4] T. Bashiri, S. M. Vaezpour, C. Park, A coupled fixed point theorem and application to fractional hybrid differential problems, Fixed Point Theory Appl., 2016 (2016), 1–11. http://dx.doi.org/10.1186/s13663-016-0511-x doi: 10.1186/s13663-016-0511-x
    [5] T. A. Burton, A fixed-point theorem of Krasnoselskii, Appl. Math. Lett., 11 (1998), 85–88. https://doi.org/10.1016/S0893-9659(97)00138-9 doi: 10.1016/S0893-9659(97)00138-9
    [6] M. Gabeleh, P. R. Patle, M. De La Sen, Noncyclic $\varphi$-contractions in hyperbolic uniformly convex metric spaces, J. Nonlinear Var. Anal., 7 (2023), 251–265. https://doi.org/10.23952/jnva.7.2023.2.06 doi: 10.23952/jnva.7.2023.2.06
    [7] D. C. Douek, M. Roederer, R. A. Koup, Emerging concepts in the immunopathogenesis of AIDS, Annu. Rev. Med., 60 (2009), 471–484. https://doi.org/10.1146/annurev.med.60.041807.123549 doi: 10.1146/annurev.med.60.041807.123549
    [8] D. J. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 11 (1987), 623–632. https://doi.org/10.1016/0362-546X(87)90077-0 doi: 10.1016/0362-546X(87)90077-0
    [9] S. M. Kang, Fixed points for expansion mappings, Math. Japonica, 38 (1993), 713–717.
    [10] M. A. Khan, M. S. Khan, S. Sessa, Some theorems on expansion mappings and their fixed points, Demonstratio Math., 19 (1986), 673–684. http://dx.doi.org/10.1515/dema-1986-0311 doi: 10.1515/dema-1986-0311
    [11] X. R. Kang, N. N. Fang, Some common coupled fixed point results for the mappings with a new contractive condition in a Menger PbM-metric space, J. Nonlinear Funct. Anal., 2023 (2023), 1–19. https://doi.org/10.23952/jnfa.2023.9 doi: 10.23952/jnfa.2023.9
    [12] A. Kari, M. Rossafi, E. M. Marhrani, M. Aamri, Fixed-point theorem for nonlinear $F$-contraction via $w$-distance, Adv. Math. Phys., 2020 (2020), 6617517. https://doi.org/10.1155/2020/6617517 doi: 10.1155/2020/6617517
    [13] A. Kari, M. Rossafi, H. Saffaj, E. M. Marhrani, M. Aamri, Fixed point theorems for $F$-contraction in generalized asymmetric metric spaces, Thai J. Math., 20 (2022), 1149–1166.
    [14] A. Kari, M. Rossafi, E. M. Marhrani, M. Aamri, New fixed point theorems for $\theta$-$\phi$-contraction on rectangular $b$-metric spaces, Abstr. Appl. Anal., 2020 (2020), 8833214. http://dx.doi.org/10.1155/2020/8833214 doi: 10.1155/2020/8833214
    [15] S. M. Kang, M. Kumar, P. Kumar, S. Kumar, Fixed point theorems for $\phi$-weakly expansive mappings in metric spaces, Int. J. Pure Appl. Math., 90 (2014), 143–152. http://dx.doi.org/10.12732/ijpam.v90i2.4 doi: 10.12732/ijpam.v90i2.4
    [16] S. Kumar, R. Kumar, J. Singh, K. S. Nisar, D. Kumar, An efficient numerical scheme for fractional model of HIV-1 infection of CD4$^+$ T-cells with the effect of antiviral drug therapy, Alex. Eng. J., 59 (2020), 2053–2064. http://dx.doi.org/10.1016/j.aej.2019.12.046 doi: 10.1016/j.aej.2019.12.046
    [17] S. Park, B. E. Rhoades, Some fixed point theorems for expansion mappings, Math. Japonica, 33 (1988), 129–132.
    [18] E. Y. Salah, B. Sontakke, M. S. Abdo, W. Shatanawi, K. Abodayeh, M. D. Albalwi, Conformable fractional-order modeling and analysis of HIV/AIDS transmission dynamics, Int. J. Differ. Equ., 2024 (2024), 1958622. https://doi.org/10.1155/2024/1958622 doi: 10.1155/2024/1958622
    [19] S. Mashayekhi, S. Sedaghat, Fractional model of stem cell population dynamics, Chaos Solitons Fract., 146 (2021), 110919. http://dx.doi.org/10.1016/j.chaos.2021.110919 doi: 10.1016/j.chaos.2021.110919
    [20] S. Ahmad, A. Ullah, A. Akgül, M. De la Sen, A study of fractional order Ambartsumian equation involving exponential decay kernel, AIMS Math., 6 (2021), 9981–9997. https://doi.org/10.3934/math.2021580 doi: 10.3934/math.2021580
    [21] V. Kiryakova, A guide to special functions in fractional calculus, Mathematics, 9 (2021), 1–40. https://doi.org/10.3390/math9010106 doi: 10.3390/math9010106
    [22] V. Kiryakova, A generalized fractional calculus and integral transforms, In: Generalized functions, convergence structures, and their applications, New York: Springer, 1988,205–217. https://doi.org/10.1007/978-1-4613-1055-6_20
    [23] X. H. Xie, Y. J. Huang, G. S. Han, Z. G. Yu, Y. L. Ma, Microbial characterization based on multifractal analysis of metagenomes, Front. Cell. Infect. Microbiol., 13 (2023), 1117421. https://doi.org/10.3389/fcimb.2023.1117421 doi: 10.3389/fcimb.2023.1117421
    [24] C. J. Silva, D. F. M. Torres, Stability of a fractional HIV/AIDS model, Math. Comput. Simulation, 164 (2019), 180–190. https://doi.org/10.1016/j.matcom.2019.03.016 doi: 10.1016/j.matcom.2019.03.016
    [25] S. Ullah, M. Altanji, M. A. Khan, A. Alshaheri, W. Sumelka, The dynamics of HIV/AIDS model with fractal-fractional Caputo derivative, Fractals, 31 (2023), 2340015. http://dx.doi.org/10.1142/S0218348X23400157 doi: 10.1142/S0218348X23400157
    [26] S. Z. Wang, B. Y. Li, Z. M. Gao, K. Iski, Some fixed point theorems on expansion mappings, Math. Japonica, 29 (1984), 631–636.
    [27] R. A. Weiss, How does HIV cause AIDS? Science, 260 (1993), 1273–1279. http://dx.doi.org/10.1126/science.8493571 doi: 10.1126/science.8493571
    [28] T. Xiang, R. Yuan, A class of expansive-type Krasnosel'skii fixed point theorems, Nonlinear Anal., 71 (2009), 3229–3239. http://dx.doi.org/10.1016/j.na.2009.01.197 doi: 10.1016/j.na.2009.01.197
    [29] B. Acay, E. Bas, T. Abdeljawad, Fractional economic models based on market equilibrium in the frame of different type kernels, Chaos Solitons Fract., 130 (2020), 109438. https://doi.org/10.1016/j.chaos.2019.109438 doi: 10.1016/j.chaos.2019.109438
    [30] S. Ahmad, A. Ullah, Q. M. Al-Mdallal, H. Khan, K. Shah, A. Khan, Fractional order mathematical modeling of COVID-19 transmission, Chaos Solitons Fract., 139 (2020), 110256. http://dx.doi.org/10.1016/j.chaos.2020.110256 doi: 10.1016/j.chaos.2020.110256
    [31] T. Alinei-Poiana, E. H. Dulf, L. Kovacs, Fractional calculus in mathematical oncology, Sci. Rep., 13 (2023), 10083. http://dx.doi.org/10.1038/s41598-023-37196-9 doi: 10.1038/s41598-023-37196-9
  • Reader Comments
  • © 2025 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
AIMS Mathematics
1.8 3.1

Metrics

Article views(603) PDF downloads(27) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog