Boundary value problem for a coupled system of nonlinear fractional differential equations. (English) Zbl 1163.34321

Su, Xinwei

Appl. Math. Lett. 22, No. 1, 64-69 (2009).

Summary: In this work we discuss a boundary value problem for a coupled differential system of fractional order. The differential operator is taken in the Riemann-Liouville sense and the nonlinear term depends on the fractional derivative of an unknown function. By means of Schauder fixed-point theorem, an existence result for the solution is obtained. Our analysis relies on the reduction of the problem considered to the equivalent system of Fredholm integral equations.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
26A33	Fractional derivatives and integrals

Keywords:

coupled system; boundary value problem; fractional derivative; existence; Green’s function; growth condition; fixed-point theorem

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