NEW CLASS OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTAL-FRACTIONAL OPERATORS: EXISTENCE, UNIQUENESS AND NUMERICAL SCHEME

Abstract

In this paper, we introduce a new fractional integro-differential equation involving newly introduced differential and integral operators socalled fractal-fractional derivatives and integrals. We present a numerical scheme that is convenient for obtaining solution of such equations. We give the general conditions for the existence and uniqueness of the solution of the considered equation using Banach fixed-point theorem. Both the suggested new equation and new numerical scheme will considerably contribute for our readers in theory and applications.