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Zbl 1208.34001
Ahmad, Bashir; Alsaedi, Ahmed
Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations. (English)
[J] Fixed Point Theory Appl. 2010, Article ID 364560, 17 p. (2010). ISSN 1687-1812/e

Summary: 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.

MSC 2000:: *34A08
34A12 Initial value problems for ODE
47N20 Appl. of operator theory to differential and integral equations

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