New existence results for fractional differential equations in a weighted Sobolev space

Abstract

In this paper, we give some conditions to prove the existence of solutions for a nonlinear boundary value problem of fractional differential equations with higher order q, (n-1< q<n), involving Riemann-Liouville fractional derivative. The solutions are discussed in a weighted fractional Riemann-Liouville Sobolev space using Schauder's fixed point theorem. An example is given to illustrate the main results.

Keywords

• fractional differential equations
• existence results
• weighted sobolev space
• fixed point theorem.