Soliton Solutions of Fractional Stochastic Kraenkel–Manna–Merle Equations in Ferromagnetic Materials

Abstract

In this study, we take into account the fractional stochastic Kraenkel–Manna–Merle system (FSKMMS). The mapping approach may be used to produce various type of stochastic fractional solutions, such as elliptic, hyperbolic, and trigonometric functions. Solutions to the Kraenkel–Manna–Merle system equation, which explains the propagation of a magnetic field in a zero-conductivity ferromagnet, may provide insight into a variety of fascinating scientific phenomena. Moreover, we construct a variety of 3D and 2D graphics in MATLAB to illustrate the influence of the stochastic term and the conformable derivative on the exact solutions of the FSKMMS.

Insights into COVID-19 stochastic modelling with effects of various transmission rates: simulations with real statistical data from UK, Australia, Spain, and India

“…Stochastic differential equations (SDEs) are a type of mathematical model used to describe the behavior of systems that are subject to randomness or unpredictability. SDEs has plenty of applications in different fields of computational science [17][18][19]. Contrary to ODEs, which depict the dynamics of deterministic systems, SDEs take into account the impacts of arbitrary disturbances, which are captured by a stochastic process.…”

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

“…Contributions by Riesz, Marchaud, Kober, Riemann-Liouville, Erdelyi, Hadamard, Grunwald-Letnikov, and Caputo have become the most recognized. A new fractional derivative categorized as the conformable derivative was just recently discovered by Mohammed et al [24]. The concept of the conformable derivative seems natural and covers most of the requirements of the classical integral derivative, such as the vanishing derivatives for constant functions, the mean value theorem, the Rolle's theorem, the chain rule, the power rule, linearity, and the quotient and product rules.…”

“…For deeper consideration of nonlinear occurrence and realistic challenges, it is essential to discover closed-form soliton solutions of SFPDEs. According to the quick advancements in nonlinear sciences, a variety of simple and efficient approaches have been developed to obtain closed-form soliton solutions to NLPDEs, including the Hirota method [4,5], the Bernoulli sub-equation method [6,7], the F-expansion method [8], the (G ′ /G 2 )-expansion method [9], the simple equation method [10], the modified auxiliary equation method [11,12], the two variable (G ′ /G, 1/G)-expansion method [13][14][15][16], the Lie symmetric analysis [17], the polynomial complete discriminant system [18], the tanh-coth scheme [19], the Conservation laws method [20], the generalized exponential rational function approach [21,22], the binary bell polynomials method [23], the mapping method [24], the Shehu transform scheme [25], the sine-Gordon expansion [26], the Cole-Hopf transformation method [27,28], the Fan subequation technique [29], the unified method [30], the Khater method [31], the r + mEDAM method [32], the spectral Tau method [33], the G ′ G ′ +G+A -expansion procedure [34][35][36][37][38], the sub-equation method [39], the collocation method [40], the finite element method [41], and the generalized G ′ /G-expansion method …”

Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system arising in ferromagnetic materials

“…In this study, we take into account the CSKMMS which is articulated as 22 : where denotes magnetization, denotes outer magnetic fields and are related to the ferrite, represents damping coefficient, is the noise intensity, B ( t ) is the Brownian motion and the operator denote conformables partial derivatives. Nguepjouo et al 23 investigated the application of magnetization density expansion and coordinate transformations to convert the structure to the following: This description encompasses the nonlinear propagation of short waves in saturated ferromagnetic materials with zero conductivity.…”