Riemann-Liouville Type Fractional Differential Equations

This work is dedicated to investigate the existence and uniqueness of solutions for nonlinear fractional differential equations with boundary conditions involving the Riemann-Liouville fractional derivative. After introducing some basic preliminaries and the important concepts of fractional calculus, we considered the model of boundary value problems of Riemann-Liouville fractional derivative. The existence and uniqueness of solution are obtained via Banach’fixed point theorem and Schauder’fixed point theorem for the two models. In addition, both results are provided by the illustrative examples to support them. Keywords: Fractional integrals and derivatives, Fractional differential equations, Existence, Uniqueness, Fixed point theorems.