Existence of the Class of Nonlinear Hybrid Fractional Langevin Quantum Differential Equation with Dirichlet Boundary Conditions

Nagamanickam Nagajothi,Vadivel Sadhasivam,Rami Ahmad El-Nabulsi,Omar Bazighifan

doi:10.3390/fractalfract5040156

Abstract

In this paper, we investigate the existence results for nonlinear fractional q-difference equations with two different fractional orders supplemented with the Dirichlet boundary conditions. Our main existence results are obtained by applying the contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also discussed.

Highlights

Fractional differential equations have been researched by a number of academics in recent years, with topics spanning from the theoretical concerns of existence and uniqueness to numerical techniques for finding solutions
Fractional differential equations have attracted a lot of attention as a result of its use in a variety of scientific and engineering applications arising from the study of precise descriptions of nonlinear processes
Several scholars have looked at hybrid fractional differential equations

Summary

Introduction

Fractional differential equations have been researched by a number of academics in recent years, with topics spanning from the theoretical concerns of existence and uniqueness to numerical techniques for finding solutions. Fractional difference equations have a wide range of applications in fields including economics, chemistry, physics and engineering. These q-fractional operators are expected to be important for the development of q-function theory, which is vital in combinatory analysis (see example [22,24,25,26,27,28]). Several generalisations of the Langevin equation with two distinct fractional orders have been developed to solve this issue, resulting in a more flexible model for fractal processes than the classic one specified by a single index. A q-variant of the nonlinear hybrid fractional Langevin equations with two distinct fractional orders complemented with Dirichlet boundary conditions has not been studied previously.

Preliminaries

Main Results

Example

Methods