Stability analysis of solutions and existence theory of fractional Lagevin equation

The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness (EU) of solutions for the prescribed equations are defined. Our viewpoint is built on the specification of the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is offered to smooth the comprehension of the hypothetical outcomes. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

This article discusses fractional Langevin equations with Caputo Hadamard-derivative, involving non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness of solutions are defined using the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is provided to facilitate the understanding of the hypothetical outcomes.