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Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving Gronwall’s inequality in Banach spaces. (English) Zbl 1299.34059

Summary: We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order \(\alpha\in (n-1,n)\) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder’s inequality, a suitable singular Gronwall’s inequality and a fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34A08 Fractional ordinary differential equations
45J05 Integro-ordinary differential equations
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