| تعداد نشریات | 32 |
| تعداد شمارهها | 860 |
| تعداد مقالات | 8,355 |
| تعداد مشاهده مقاله | 52,929,532 |
| تعداد دریافت فایل اصل مقاله | 9,317,475 |
Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study | ||
| Journal of Mathematical Modeling | ||
| مقاله 9، دوره 13، شماره 2، مرداد 2025، صفحه 375-391 اصل مقاله (209.7 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.29126.2594 | ||
| نویسندگان | ||
| Samira Zerbib* ؛ Khalid Hilal؛ Ahmed Kajouni | ||
| LMACS Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco | ||
| چکیده | ||
| The objective of this work is to investigate the existence and uniqueness of the solution to a nonlinear fractional integro-differential equation with a non-local condition involving the generalized fractional proportional Caputo derivative of two distinct orders. To achieve this, Krasnoselskii’s fixed point theorem is utilized to examine the existence of the solution, followed by the application of Banach’s fixed point theorem to study the uniqueness. Lastly, two illustrative examples are provided to highlight the main results. | ||
| کلیدواژهها | ||
| Differential equation؛ generalized Caputo proportional fractional derivative؛ non-local condition؛ fixed point theorem | ||
| مراجع | ||
|
[1] A. Atangana, D. Baleanu, New fractional derivative with non-local and non-singular kernel, Therm. Sci. 20 (2016) 757. [2] T.A. Burton, Fixed-point theorem of Krasnoselskii, Appl. Math. Lett. 11 (1998) 85-88. [3] M. Bohner, S. Hristova, Stability for generalized Caputo proportional fractional delay integro- differential equations, Bound. Value Probl. 2022 (2022) 14. [4] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2015) 73–85. [5] S.A. David, J.L. Linares, E.M.D.J.A. Pallone, Fractional order calculus: historical apologia, basic concepts and some applications, Rev. Bras. Ensino Fis. 33 (2011) 4302–4302. [6] R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Springer Vienna, 1997 [7] K. Hilal, A. Kajouni, S. Zerbib, Hybrid fractional differential equation with nonlocal and impulsive conditions, Filomat 37 (2023) 3291–3303. [8] F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modification J. Nonlinear Sci. Appl. 10 (2017) 2607–2619. [9] F. Jarad, T. Abdeljawad, Z. Hammouch, On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative, Chaos Solit. Fractals 117 (2018) 16–20. [10] F. Jarad, T. Abdeljawad, S. Rashid, Z. Hammouch, More properties of the proportional fractional integrals and derivatives of a function with respect to another function, Adv. Differ. Equ. 2020 (220) 303. [11] F. Jarad, M.A. Alqudah, T. Abdeljawad, On more general forms of proportional fractional opera- tors, Open Math. 18 (2020) 167–176. [12] I. Mallah, I. Ahmed, A. Akgul, F. Jarad, S. Alha, On ψ-Hilfer generalized proportional fractional operators, AIMS Math. 7 (2021) 82–103. [13] M. Mebrat, G.M.N. Guerekata, A Cauchy problem for some fractional differential equation via deformable derivatives J. Nonlinear Evol. Equ. Appl. 4 (2020) 55–63. [14] U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput. 218 (2011) 860–865. [15] U.N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl. 6 (2014) 1–15. [16] I. Podlubny, Matrix approach to discrete fractional calculus, Fract. Calc. Appl. Anal. 3 (2000) 359–386. [17] K. Shah, M.A. Alqudah, F. Jarad, T. Abdeljawad, Semi-analytical study of pine wilt disease model with convex rate under Caputo-Fabrizio fractional order derivative,Chaos Solit. Fractals 135 (2020) 109754. [18] A. Rahmani, W.S. Du, M.T. Khalladi, M. Kostic, D. Velinov, Proportional Caputo Fractional Dif- ferential Inclusions in Banach Spaces, Symmetry 14 (2022) 1941. [19] S.Z. Rida, A.M.A. El-Sayed, A.A.M. Arafa, Effect of bacterial memory dependent growth by using fractional derivatives reaction-diffusion chemotactic model, J. Stat. Phys. 140 (2010) 797–811. [20] H.G. Sun, W. Chen, H. Wei, Y.Q. Chen, A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems, Eur. Phys. J. Spec. Top. 193 (2011) 185–192. [21] R. Sreedharan, S.R. Balachandar, R. Udhayakumar, S. Etemad, I. Avc, S. Rezapour, On the frac- tional perturbed neutral integro-differential systems via deformable derivatives: an existence study, Bound. Value Probl. 2024 (2024) 74. [22] M. Yavuz, N. Ozdemir, Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel, Discrete Contin. Dyn. Syst. 13 (2020) 995–1006. [23] M. Yavuz, N. Ozdemir, European vanilla option pricing model of fractional order without singular kernel, Fractal Fract. 2 (2018) 3. [24] S. Zerbib, N. Chefnaj, K. Hilal, A. Kajouni, Study of p-Laplacian hybrid fractional differential equations involving the generalized Caputo proportional fractional derivative, Comput. Methods. Differ Equ., 2024, https://doi.org/10.22034/cmde.2024.61552.2665. [25] S. Zerbib, K. Hilal, A. Kajouni, Some new existence results on the hybrid fractional differential equation with variable order derivative, Results Nonlinear Anal. 6 (2023) 34–48. | ||
|
آمار تعداد مشاهده مقاله: 363 تعداد دریافت فایل اصل مقاله: 428 |
||