The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, numerical models for simulation harbors shallow seas. In this article, the sine-Gordon expansion (SGE) approach generalized Kudryashov (GK) scheme are to establish broad-spectral solutions including unknown parameters typical analytical recovered as a special case. well-known bell-shape soliton, kink, singular compacton, contracted periodic anti-bell shape...

This paper studies the optical soliton solutions of a nonlinear Schrödinger equation (NLSE) involving parabolic law nonlinearity with presence dispersion by using generalized auxiliary technique. As result, new varieties exact traveling wave have been uncovered, comprising hyperbolic trigonometric, exponential, and rational. Interestingly, we obtain bright, dark, periodic, singular, other to model. Some achieved are illustrated graphically in order fully understand their physical behaviour....

In this article, we analyse the numerical simulation of time-fractional Black-Scholes model governing butterfly spread option, digital option and double barrier option. For purpose, a local meshless collocation method based on multiquadric radial basis function is used. The equation discretized in temporal sense by Liouville-Caputo fractional derivative scheme for 0<β<1, whereas space derivatives are suggested method. Numerical experiments performed Efficiency accuracy proposed assessed...

The aim of this study is to provide the numerical outcomes a nonlinear HIV infection system latently infected CD4+ T cells exists in bioinformatics using Morlet wavelet (MW) artificial neural networks (ANNs) optimized initially with global search genetic algorithms (GAs) hybridized for speedy local sequential quadratic programming (SQP), i.e., MW-ANN-GA-SQP. design an error function presented by designing MW-ANN models differential equations along initial conditions that represent involving...

In this paper, we studied the Drinfel'd–Sokolov–Wilson equation (DSWE) and Boiti Leon Pempinelli (BLPE) in conformable sense. The sine–cosine method is utilized to achieve various traveling wave solutions suggested nonlinear systems. It an easy approach use does not require sophisticated mathematical software or a knowledgeable coder. can also be used for linear fractional issues, making it pervasive. obtained form of solitons emerge with necessary constraints ensure their existence. results...

It is generally considered that fractal-fractional order derivative operators are highly sophisticated mathematical tools can be applied in a variety of physics and engineering situations to obtain real solutions. By using derivatives, we simultaneously investigate fractional fractal dimension. Due extensive applications the present article model non-linear Couple stress nanofluid has been analyzed. The homogenous mixture base fluid nanoparticles formed by uniform dispersion cadmium...

In this work, we apply three different techniques to solve the Fitzhugh-Nagumo equation that is an important used describe propagation of electrical signals in excitable media, such as nerve fibers. Residual power series method (RPSM), homotopy perturbation (HPM), and a modified fractional Taylor expansion, are applied nonlinear obtain approximate solutions. By comparing exact solution with solutions obtained from methods suggested demonstrate these efficient tools partial differential...

In this paper, a new solution process of ( 1 / G ′ ) -expansion and , methods has been proposed for the analytic Zhiber-Shabat (Z-S) equation. Rather than classical method, function in different formats produced with help process. New complex rational, hyperbolic, rational trigonometric types solutions Z-S equation have constructed. By giving arbitrary values to constants obtained solutions, it can add physical meaning traveling wave whereas an important place applied sciences illuminates...

Snow is of porous structure and good thermal insulation property. A fractal derivative model established to reveal its property, it extremely high thermal-stable, the whole snow will not be affected much by sudden environmental temperature change. simple experiment carried out verify theoretical finding, result helpful design advanced materials mimicking structure.

The study of nonlinear phenomena associated with physical is a hot topic in the present era. fundamental aim this paper to find iterative solution for generalized quintic complex Ginzburg–Landau (GCGL) equation using fractional natural decomposition method (FNDM) within frame calculus. We consider projected equations by incorporating Caputo operator and investigate two examples different initial values efficiency applicability FNDM. presented nature obtained results defined three distinct...

In this article, we presented an efficient local meshless method for the numerical treatment of two term time fractional-order multi-dimensional diffusion PDE. The demand techniques increment because its nature and simplicity usage in higher dimensions. This technique approximates solu?tion on set uniform scattered nodes. space derivatives models are discretized by proposed procedure though fractional part is Liouville-Caputo derivative. re?sults obtained 1-, 2- 3-D cases rectangular...

Higher order and multidimensional generalizations of the nonlinear Schrödinger equation are useful in a variety applications. A generalized (3+1)-dimensional Sasa–Satsuma is studied via improved Riccati mapping method its Bäcklund transformation extended hyperbolic function method. This model can be use to describe physical processes wave propagation optical fibers. We explicitly retrieved varieties solitons like bright, dark, singular, combined bright–dark singular-bright this model. Other...

In this article, we also introduced two well-known computational techniques for solving the time-fractional Fornberg–Whitham equations. The methods suggested are modified form of variational iteration and Adomian decomposition by ρ-Laplace. Furthermore, an illustrative scheme is to verify accuracy available methods. graphical representation exact derived results presented show approaches reliability. comparative solution analysis via graphs represented higher reliability current techniques.

The current research is about new exact soliton solutions to the Cahn–Allen equation and Predator–Prey model with most general fractional derivative operator. novel truncated M-fractional applied study aforementioned models secure via modified integration scheme known as extended Sinh–Gordon expansion method (ShGEEM). This provides dark, singular, singular-dark, kink solitons other certain conditions. gained results are also verified use of symbolic software. obtained may be in demonstration...

Abstract The variant Boussinesq equation has significant application in propagating long waves on the surface of liquid layer under gravity action. In this article, improved Bernoulli subequation function (IBSEF) method and new auxiliary (NAE) technique are introduced to establish general solutions, some fundamental soliton solutions accessible literature, archetypal solitary wave that extracted from broad-ranging solution equation. established knowledgeable obtained as a combination...

In this study, disparate analytical methodologies like the tan method, rational Exp-function sech extended and sine–cosine method are implemented to solve double Sine-Gordon equation (DSG). Subsequently, dynamical attributes of obtained results have been underlined depicted in terms 3D 2D graphical illustrations, likewise, different soliton solutions such as kink, bright-dark, bright under an appropriate selection parameters, existing criteria these solitons also given. A Survey literature...

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse dynamics of chaotic system based on a circuit design. The problem modelled in terms classical order nonlinear, coupled ordinary differential equations which then generalized through kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability have been calculated. highly non-linear fractal-fractional analyzed numerical technique...

In this work, it is used three families of nonlinearities such as Kerr law, Power Law and Parabolic law over the High-order dispersive Nonlinear Schrödinger equation to inquire optical soliton solutions diverse by employing Sardar Sub-equation method. Considering constraint relation on some parameters NLSE, obtained bright dark solutions. However, under a certain condition method parameters, exposed singular trigonometric function More precisely, for ρ=a24b, new form complex are obtained....

He’s multiple scales method is a couple of the homotopy perturbation and technology in classic method. This has been proved to be powerful mathematical tool various nonlinear equations, it extremely effective for forced oscillators. paper shows that can further improved by incorporating some known technologies, e.g., parameter-expanding technology, enhanced with an auxiliary term. Due wide application method, cleans solutions equations while fails.

Both fibroin-based and sericin-based biomaterials have been studying extensively due to their wide applications, however the extraction of either fibroin or sericin protein is extremely complicated. Here we prepare solution directly from alive silkworms instead extracting proteins silkworm silk. The polyvinyl alcohol are mixed in different weight ratios produce silkworm-based silk fibers, which many special properties like high mechanical strength good wetting property. new production has...

In this paper, porous chamber with considering nanomaterial as operating fluid has been scrutinized. The transportation of nanopowder was controlled by magnetic force and insert media boosts the cooling rate. Such zone needs special model to involve impact in non-Darcy technique utilized. Low fraction hybrid leads good accuracy homogeneous empirical correlations have employed forecast features fluid. Entropy generation studied find influence each term on irreversibility unit. Also, two...

The main objective of this paper is to establish new oscillation results solutions a class fourth-order advanced differential equations with delayed arguments. key idea our approach use the Riccati transformation and theory comparison first second-order delay equations. Four examples are provided illustrate results.

Abstract The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) obtain numerical solutions different types fifth-order Korteweg-de Vries (KdV) equations. In order assess precision, stability accuracy solutions, five test problems are offered for KdV Numerical results compared with Adomian decomposition method, Laplace method homotopy perturbation transform which reveals that MVIA-II exceptionally productive,...

The current work deals with the study of a thermo-piezoelectric modified model in context generalized heat conduction memory-dependent derivative. investigations limited-length piezoelectric functionally graded (FGPM) rod have been considered based on presented model. It is assumed that specific and density are constant for simplicity while other physical properties FGPM to vary exponentially through length. subject moving source along axial direction fixed zero voltage at both ends. Using...

This article examines the coupled KdV equations and system of variant Boussinesq with beta time derivative explores their travelling wave solutions. work explains evolution waves fractional parameter. The simple ansatz approach produces a variety novel solutions in terms hyperbolic periodic functions. Graphical representation are also presented.