On the ψ-Hilfer fractional derivative

In this paper we introduce a new fractional derivative with respect to another function the so-called ψ-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some results involving uniformly convergent sequence of function, uniformly continuous function and examples including 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 ψ-Hilfer fractional derivative.