Existence and Uniqueness of Solutions for Initial Value Problems of Caputo Fractional Order Ordinary Differential Equation

Abstract

This research is intended to study the relationship between the fractional order integral of a function the Riemann-Liouville fractional order derivative of the function and the Caputo fractional order derivative of the function and also to prove the existence and uniqueness of solutions for initial value problems (IVP) of Caputo fractional order ordinary differential equations using Schaefer fixed point theorem.