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Existence of positive solutions for \(m\)-point boundary value problem for nonlinear fractional differential equation. (English) Zbl 1222.34006

Summary: We investigate an \(m\)-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given, and some useful properties of the Green function are obtained. By using the fixed-point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem, the existence of multiple positive solutions is obtained.

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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