Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

Abstract

We study a boundary value problem of fractional integrodifferential equations involving Caputo's derivative of order α ∈ (n − 1, n) in a Banach space. Existence and uniqueness results for the problem are established by means of the Hölder's inequality together with some standard fixed point theorems.

A study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative

“…In [10], the existence of solutions of fractional IDEs by using the resolvent operators and fixed point theorem are proved. Existence results for boundary value problems of arbitrary order IDEs in Banach spaces was studied by K. Karthikeyan and Bashir Ahmad [21]. For some investigations on fractional IDEs, one can refer to [5,8,9,22].…”