Existence of Solutions for a Coupled System of Ψ-Caputo Fractional Differential Equations With Integral Boundary Conditions

被引：1
作者：
Poovarasan, R. [1 ]
Govindaraj, V. [1 ]
机构：
[1] Natl Inst Technol Puducherry, Dept Math, Karaikal, India
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年
关键词：
coupled system; fractional boundary value problem; integral boundary condition; psi-Caputo derivative; RESPECT;
D O I：
10.1002/mma.10810
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, we examine a system of fractional differential equations involving nonlinear terms that depend on unknown functions and their fractional derivatives. We propose coupled nonlocal boundary conditions with integral constraints, introducing a novel problem within fractional calculus and nonlinear dynamics. Our main contributions include proving the existence of solutions obtained via Leray-Schauder's alternative and establishing uniqueness via the contraction mapping principle. These findings are further supported by examples that showcase the system's mathematical properties and behavior.
引用
收藏
页数：13
相关论文
共 26 条
  • [1] Podlubny I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, (1998)
  • [2] Klafter J., Lim S.C., Metzler R., Fractional Dynamics: Recent Advances, (2012)
  • [3] Sabatier J.A.T.M.J., Agrawal O.P., Machado J.A.T., Advances in Fractional Calculus, 4, (2007)
  • [4] Machado J.T., Kiryakova V., Mainardi F., Recent History of Fractional Calculus, Communications in Nonlinear Science and Numerical Simulation, 16, 3, pp. 1140-1153, (2011)
  • [5] Odibat Z., Baleanu D., Numerical Simulation of Initial Value Problems With Generalized Caputo-Type Fractional Derivatives, Applied Numerical Mathematics, 156, pp. 94-105, (2020)
  • [6] Feldman D.E., Halperin B.I., Fractional Charge and Fractional Statistics in the Quantum Hall Effects, Reports on Progress in Physics, 84, 7, (2021)
  • [7] Almeida R., A Caputo Fractional Derivative of a Function With Respect to Another Function, Communications in Nonlinear Science and Numerical Simulation, 44, pp. 460-481, (2017)
  • [8] Almeida R., Malinowska A.B., Monteiro M.T.T., Fractional Differential Equations With a Caputo Derivative With Respect to a Kernel Function and Their Applications, Mathematical Methods in the Applied Sciences, 41, 1, pp. 336-352, (2018)
  • [9] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, 204, (2006)
  • [10] Zaky M.A., Hendy A.S., Suragan D., A Note on a Class of Caputo Fractional Differential Equations With Respect to Another Function, Mathematics and Computers in Simulation, 196, pp. 289-295, (2022)
123