On a generalization of fractional Langevin equation

TL;DR

This paper introduces a generalized fractional Langevin equation with boundary conditions, establishing existence and uniqueness of solutions, and showing that previous models are special cases of this broader framework.

Contribution

It extends fractional Langevin equations to a more general form with boundary conditions, providing new theoretical results on solutions.

Findings

Existence and uniqueness of solutions proved.

Previous fractional Langevin models are special cases.

Framework broadens understanding of fractional stochastic processes.

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 results of the fixed point theory. Moreover, the previous results of fractional Langevin equations are a special case of our problem.