On a fractional differential equation with fractional boundary conditions

Abstract

In this article, we study a new nonlinear Langevin equation of two fractional orders with fractional boundary value conditions which is a generalization of previous Langevin equations. Based on Banach and Schauder fixed point theorems, the existence and uniqueness of solutions of this equation are investigated. Moreover, our hypotheses are simpler than similar works.

Keywords

• fractional langevin equation
• fractional boundary condition
• existence solution
• fixed point theorem