A study of a coupled system of fractional differential equation swith Caputo-Fabrizio fractional derivative

• Autorzy: Salima Mansouri , Bekkouche Mohammed Moumen

Identyfikatory

DOI

10.17512/jamcm.2025.4.06

• Języki publikacji: EN

Abstrakty

EN

In this study, we discuss the existence and uniqueness of solutions to a coupled system of nonlinear fractional differential equations of the Caputo-Fabrizio type with boundary conditions. We prove the existence and uniqueness of the solution using Banach’s f ixed-point theorem and the Leray-Schauder alternative theorem. Finally, we support our study with two illustrative examples.

Słowa kluczowe

EN

Caputo-Fabrizio fractional derivative; Caputo-Fabrizio integral of fractional order; fractional differential equation; fractional integral; coupled system; fixed point

PL

pochodna ułamkowa Caputo-Fabrizio; całka Caputo-Fabrizia rzędu ułamkowego; równanie różniczkowe ułamkowe; całka ułamkowa; układy sprzężone; punkt stały

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 4
• Strony: 85--99
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Salima Mansouri

• Laboratoire de Theorie des Operateurs - et EDP (fondements et applications) Department of Mathematics, El oued University, 39000 El oued, Algeria

autor

Bekkouche Mohammed Moumen

• Laboratoire de Theorie des Operateurs - et EDP (fondements et applications) Department of Mathematics, El oued University, 39000 El oued, Algeria

Bibliografia

• [1] Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85. DOI: 10.12785/pfda/ 010201.
• [2] Losada, J., & Nieto, J.J. (2015). Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 87-92. DOI: 10.12785/pfda/010202.
• [3] Almeida, R. (2017). A Caputo fractional derivative of a function with respect to another function. Communication of Nonlinear Science and Numerical Simulation, 44, 460-481. DOI: 10.1016/ j.cnsns.2016.09.006.
• [4] Hristov, J. (2018). The non-singular kernel derivative: A tool for modeling memory-dependent phenomena without singularities. Journal of Thermal Stresses, 41(1), 1-21.
• [5] Baleanu, D., et al. (2019). On nonlocal integral and derivative boundary conditions in fractional differential equations. Mathematical Methods in the Applied Sciences, 42(13), 4478-4490.
• [6] Goodrich, C.S. (2013). On nonlocal BVPs with nonlinear boundary conditions. Applied Mathe matics Letters, 26(10), 1020-1025.
• [7] Bekkouche, M.M., & Guebbai, H. (2020). Analytical and numerical study for a fractional bound ary value problem with a conformable fractional derivative of Caputo and its fractional integral. Journal of Applied Mathematics and Computational Mechanics, 19(2), 31-42. DOI: 10.17512/ jamcm.2020.2.03.
• [8] Granas, A., & Dugundji, J. (2003). Fixed Point Theory. New York: Springer-Verlag.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).