On the Novel Existence Results of Solutions for Fractional Langevin Equation Associating with Nonlinear Fractional Orders

Wutiphol Sintunavarat, Ali Turab

Abstract

The Langevin equation is a core premise of the Brownian motion, which describes the development of essential processes in continuously changing situations. As a generalization of the classical one, the fractional Langevin equation offers a fractional Gaussian mechanism with two indices as parametrization, which is more flexible to model fractal systems. This paper aims to deals with a nonlinear fractional Langevin equation that involves two fractional orders with nonlocal integral boundary conditions. Our goal is to find the results related to the existence of solutions for the proposed Langevin equation by using the appropriate fixed point methods. An example is also presented to illustrate the importance of our result.