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A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices. (English) Zbl 1275.34005
Summary: This paper is devoted to a study of a nonlocal boundary value problem for a nonlinear differential equation depending on two fractional orders \(\alpha,\beta\in(1,2]\). The problem is inverted and an equivalent integral equation is constructed; as applications, the contraction mapping principle and a Krasnosel’skii fixed point theorem are applied to obtain sufficient conditions for the existence of solutions. An example illustrates the results. In the case that \(\alpha=\beta=2\), results for fourth order ordinary differential equations are obtained.

MSC:
34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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