Existence of solutions for a nonlocal fractional boundary value problem. (English) Zbl 1397.34021

Summary: We study a nonlinear fractional boundary value problem with nonlocal boundary conditions. An associated Green’s function is constructed as a series of functions by the perturbation approach. Criteria for the existence of solutions are obtained based upon it.


34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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