Existence result for a fractional differential equation involving a special derivative

Abstract

<jats:title>Abstract</jats:title>
<jats:p>In this article, we establish certain sufficient conditions to show the existence of solutions of an initial value problem of fractional-ordinary differential equation in Banach space. Our approach is based on a combination of Mönch fixed point theorem and a suitable measure of non-compactness. Also an example is given to illustrate our approach.</jats:p>