Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

Painlevé analysis,auto-Bäcklund transformation and new exact solutions of(2+1)and(3+1)-dimensional extended Sakovich equation with time dependent variable coefficients in ocean physics

This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the considered equations.Painlevéanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations.Two new family of exact analytical solutions are being obtained success-fully for each of the considered equations.The soliton solutions in the form of rational and exponential functions are being depicted.The results are also expressed graphically to illustrate the potential and physical behaviour of both equations.Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.

New Exact Solutions of Fractional Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations Using Fractional Sub-Equation Method

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.

New exact solutions of coupled Boussinesq-Burgers equations by Exp-function method

In the present paper,we build the new analytical exact solutions of a nonlinear differential equation,specifically,coupled Boussinesq-Burgers equations by means of Exp-function method.Then,we analyze the results by plotting the three dimensional soliton graphs for each case,which exhibit the simplicity and effectiveness of the proposed method.The primary purpose of this paper is to employ a new approach,which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq-Burgers equations.

Two efficient reliable methods for solving fractional fifth order modified Sawada-Kotera equation appearing in mathematical physics

The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera equations.As a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera equation.We have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.

A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrdinger–Boussinesq Equations Involving Riesz Fractional Derivative

In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.

New Optical Soliton Solutions of Nolinear Evolution Equation Describing Nonlinear Dispersion

In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function.The Petrov-Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically.The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method(VIM)and exact solutions.For fractional order,the numerical outcomes of fractional Sharma-Tasso-Olver equations are also compared with those obtained by variational iteration method(VIM)in Song et al.[Song L.,Wang Q.,Zhang H.,Rational approximation solution of the fractional Sharma-Tasso-Olver equation,J.Comput.Appl.Math.224:210-218,2009].Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.

New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation

In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.

Painlevéintegrability,auto-Bäcklund transformations,new abundant analytic solutions including multi-soliton solutions for time-dependent extended KdV8 equation in nonlinear physics

In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant level.These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation.These solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton solutions.Multi-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered equation.All the results are being expressed graphically to signify the physical importance of the considered equation.