Existence and stability results for fractional integro-differential equation  with Hilfer fractional derivative

Rima Faizi

doi:10.5269/bspm.63375

Rima Faizi University of Mohammed seddik benyahia, Jijle, Algeria.

Abstract

In this paper, we discuss the existence, uniqueness of solutions and Ulam-Hyers stability for the Hilfer fractional integro-differential equation with nonlocal Erdélyi-Kober fractional condition. First, the equivalence of this class of problem and a nonlinear Volterra integral equation is established. Next, the existence and uniqueness results are obtained by using a variety of fixed point theorems, such as Banach's and Krasnoselskii's fixed point theorems. Further, due to the Gronwall inequality, we obtain Ulam-Hyers stability of the considered problem. Finally, two examples are given to illustrate our theory results.

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