Volume 11, Issue 2
Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative

Adv. Appl. Math. Mech., 11 (2019), pp. 338-359.

Published online: 2019-01

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• Abstract

Considering a fractional integro-differential equation involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem. An example is provided to illustrate our main results.

• Keywords

Fractional integro-differential equations $\psi$-Hilfer fractional derivative and $\psi$-fractional integral existence uniqueness and Ulam-Hyers stability Fixed point theorem.

34K37 26A33 34A12 47H10

@Article{AAMM-11-338, author = {Mohammed S. Abdo and Satish K. Panchal}, title = {Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {338--359}, abstract = {