Existence of Solutions for Fractional Langevin Equation Involving Generalized Caputo Derivative with Periodic Boundary Conditions

摘要

In this article, we investigate the existence and uniqueness(EU) of solutions for non-linear Langevin fractional differential equation (FDEs) in term of generalized Caputo fractional derivative(GCFD) of two distinct orders with periodic boundary conditions involving generalized fractional differential operator. The existence result is derived by applying Krasnoselskii＇s fixed point theorem and the uniqueness of solution is determined by using Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.