FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND Ψ–HILFER FRACTIONAL DERIVATIVE

In this paper, we consider a fractional integro-differential equation with nonlocal condition involving a general form of Hilfer fractional derivative. We show that Cauchy-type problem is equivalent to a Volterra fractional integral equation. We also employ the Banach fixed point theorem and Krasnoselskii’s fixed point theorem to obtain existence and uniqueness of solutions. Ulam-Hyers-Rassias stability results are established. Further, Mittag-Leffler least squares method is used to approximate the resulting nonlinear implicit analytic solution of the problem. An example is provided to illustrate our main results.