Existence result for a fractional differential equation involving a special derivative

Abstract

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.

Keywords

• fractional-ordinary differential equation
• measure of non-compactness of kuratowski
• banach space
• mönch fixed point theorem
• riemann-liouville fractional derivative
• 26a33
• 34a08
• 47h10