On the $\psi$-Hilfer fractional derivative

Abstract

In this paper we introduce a new fractional derivative with respect to another function the so-called $\psi$-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some uniformly convergent sequence of function results and examples involving the Mittag-Leffler function with one parameter. Finally, we present a wide class of integrals and fractional derivatives, by means of the fractional integral with respect to another function and the $\psi$-Hilfer fractional derivative.