Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

Fixexd point theory and applications

Bashir Ahmad¹  Ahmed Alsaedi¹ 

[1] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: Couple System;    Fractional Order;    Fractional Derivative;    Fractional Calculus;    Fractional Differential Equation;   

DOI  :  10.1155/2010/364560

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

【 授权许可】

CC BY