On the singular-hybrid type of the Langevin fractional differential equation with a numerical approach

Abstract

Abstract The nonlinear fractional Langevin equation is an important equation used in various areas of physics and mathematics. In this article, we focus on the singular-hybrid case of the generalized Langevin equations and prove the existence of a solution using fixed point theory. We also provide numerical and graphical simulations to demonstrate the convergence and existence of a solution for this singular problem. Finally, we present numerical examples in the form of tables and graphs to examine the accuracy of the method.

Keywords

• Caputo derivative
• Fractional Langevin equation
• Hybrid problem
• Singularity