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

Preview Purchase PDF 12 2425
Export citation

Cited by

• 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.