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

By Bashir Ahmad, Ahmed Alsaedi. 2010

70 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ad0c2fa4ebebea6d3c340894b92a6b780ac2dddf

Citations in the corpus

• Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions (2011, unknown): “For some recent development on the topic, (see [3-19] and references therein).”