Boundary value problem for a coupled system of nonlinear fractional differential equations.

*(English)*Zbl 1163.34321Summary: 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
Full Text:
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##### References:

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