On a generalization of fractional Langevin equation with boundary conditions

Abstract

In this work, we consider a generalization of the nonlinear Langevin equation of fractional orders with boundary value conditions. The existence and uniqueness of solutions are studied by using the results of the fixed point theory. Moreover, the previous results of fractional Langevin equations are a special case of our problem.

Keywords

• nonlinear langevin equation
• fractional order
• existence of solution