The Influence of Noise on the Exact Solutions of the Stochastic Fractional-Space Chiral Nonlinear Schrödinger Equation

Wael W Mohammed,Omar Bazighifan,A Othman Almatroud,Mohammed M Al-Sawalha,Elkhateeb S Aly

doi:10.3390/fractalfract5040262

Abstract

In this paper, we consider the stochastic fractional-space Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived via multiplicative noise. We obtain the exact solutions of the S-FS-CNSE by using the Riccati equation method. The obtained solutions are extremely important in the development of nuclear medicine, the entire computer industry and quantum mechanics, especially in the quantum hall effect. Moreover, we discuss how the multiplicative noise affects the exact solutions of the S-FS-CNSE. This equation has never previously been studied using a combination of multiplicative noise and fractional space.

Highlights

The fractional derivatives may be used to represent many physical phenomena in electromagnetic theory, signal processing, mathematical biology, engineering applications and different scientific disciplines
The fractional derivative has been utilized in the disciplines of finance [1,2,3], biology [4,5,6], physics [7,8,9,10,11], hydrology [12,13]
In this paper, we take into account the following stochastic fractionalspace Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived in the Itô sense by multiplicative noise in this form

Summary

Introduction

The fractional derivatives may be used to represent many physical phenomena in electromagnetic theory, signal processing, mathematical biology, engineering applications and different scientific disciplines. In this paper, we take into account the following stochastic fractionalspace Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived in the Itô sense by multiplicative noise in this form. Equation (1) with ρ = 0 is a kind of nonlinear evolution equation found in many fields of applied research, including nonlinear quantum mechanics, plasma physics, and optics It produces chiral solitons, which play a significant role in the quantum-hall effect. The originality of this article is to obtain the exact stochastic fractional solutions of the S-FS-CNSE (1) forced by multiplicative noise by using the Riccati equation method. To add more to our knowledge, this is the first paper that uses a combination of multiplicative noise and fractional space to obtain the exact solution of the S-FS-CNSE (1).

Modified Riemann–Liouville Derivative and Properties

Wave Equation for S-FS-CNSE Equation

The Exact Solutions of the S-FS-CNSE

The Effect of Noise on the Solutions of S-FS-CNSE

Conclusions