<abstract><p>In this paper, we find the solution of time-fractional Newell-Whitehead-Segel equation with help two different methods. The newell-Whitehead-Segel plays an efficient role in nonlinear systems, describing stripe patterns' appearance two-dimensional systems. Four case study problems are solved by proposed methods aid Antagana-Baleanu fractional derivative operator and Laplace transform. numerical results obtained suggested techniques compared exact solution. To show...

The present research investigates symmetric soliton solutions for the Fractional Coupled Konno–Onno System (FCKOS) by using two improved versions of an Extended Direct Algebraic Method (EDAM) i.e., modified EDAM (mEDAM) and r+mEDAM. By obtaining precise analytical solutions, this explores characteristics behaviours solitons in FCKOS. Further, amplitude, shape propagation behaviour some are visualized means a 3D graph. This investigation fosters more thorough comprehension non-linear wave...

In this investigation, we utilize advanced versions of the Extended Direct Algebraic Method (EDAM), namely modified EDAM (mEDAM) and r+ mEDAM, to explore families optical soliton solutions in Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model (FPRKLM). Our study stands out due its in-depth investigation identification multiple localized stable families, illuminating their complex behavior. We offer visual validation via carefully designed 3D graphics that capture behaviors these...

This research uses a novel analytical method known as the modified Extended Direct Algebraic Method (mEDAM) to explore families of soliton solutions for complex structured Coupled Fractional Biswas–Arshed Model (CFBAM) in Birefringent Fibers. The (DAM) is extended by mEDAM’s methodology compute more that would otherwise be difficult acquire. We use this derive several and examine their characteristics. also look at how different model parameters, such amplitude, width, propagation speed,...

In this paper, we study the numerical solution of fractional Jaulent–Miodek equations with help two modified methods: coupled variational iteration transformation technique and Adomian decomposition technique. The equation has applications in several related fields physics, including control theory dynamical systems, anomalous transport, image signal processing, financial modelings, nanotechnology, viscoelasticity, nanoprecipitate growth solid solutions, random walk, modeling for shape...

Abstract This work dives into the Conformable Stochastic Kraenkel-Manna-Merle System (CSKMMS), an important mathematical model for exploring phenomena in ferromagnetic materials. A wide spectrum of stochastic soliton solutions that include hyperbolic, trigonometric and rational functions, is generated using a modified version Extended Direct Algebraic Method (EDAM) namely r +mEDAM. These have practical relevance describing magnetic field behaviour zero-conductivity ferromagnets. By Maple to...

Damped Burger’s equation describes the characteristics of one-dimensional nonlinear shock waves in presence damping effects and is significant fluid dynamics, plasma physics, other fields. Due to potential applications this equation, thus objective investigation solve analyze time fractional form using methods with precise efficiency, high accuracy, ease application calculation, flexibility dealing more complicated equations, which are called Aboodh residual power series method transform...

In the present article, we related analytical solution of fractional-order dispersive partial differential equations, using Laplace–Adomian decomposition method. The Caputo operator is used to define derivative fractional-order. method solutions for both fractional and integer orders are obtained in series form, showing higher convergence proposed Illustrative examples considered confirm validity order that convergent also investigated.

In this paper, the Elzaki transform decomposition method is implemented to solve time-fractional Swift–Hohenberg equations. The presented model related temperature and thermal convection of fluid dynamics, which can also be used explain formation process in liquid surfaces bounded along a horizontally well-conducting boundary. Caputo manner, fractional derivative described. suggested easy implement needs small number calculations. validity confirmed from numerical examples. Illustrative...

In this article, we find the solution of time‐fractional Belousov–Zhabotinskii reaction by implementing two well‐known analytical techniques. The proposed methods are modified form Adomian decomposition method and homotopy perturbation with Yang transform. Caputo manner, fractional derivative is used. obtained in series which helps investigating (B‐Z) system. To verify accuracy methods, an illustrative example taken, through graphs, shown. Also, fractional‐order integer‐order solutions...

In this paper, we find the solution of fractional-order Kaup–Kupershmidt (KK) equation by implementing natural decomposition method with aid two different fractional derivatives, namely Atangana–Baleanu derivative in Caputo manner (ABC) and Caputo–Fabrizio (CF). When investigating capillary gravity waves nonlinear dispersive waves, KK is extremely important. To demonstrate accuracy efficiency proposed technique, study three distinct cases. The results are given form a series, which converges...

This research looked at the unsteady free convection flows of an incompressible viscous fluid with heat/sink in a vertical cylinder containing mixture 47 nm alumina nanoparticles water. The flow direction is subjected to perpendicular magnetic field. generalization entails taking into account new version constitutive equation for thermal flux, known as generalized Atangana-Baleanu derivative, which based on time-fractional derivative Mittag-Leffler kernel. Using Laplace transform and finite...

This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. method combines Zain Ul Abadin Zafar-transform (ZZ-T) and (HPT) show validation efficiency of this investigate three examples. It is also shown that fractional integer-order solutions have closed contact with exact result. The suggested found be reliable, efficient, straightforward use for many related models...

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination transformation and technique, we achieve analytic approximation results in rapid convergent form by employing notion limit, with less time effort than method. Three challenges are evaluated simulated to validate suggested method’s practicability, efficiency, simplicity....

<abstract><p>The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Vries system is obtained in this study by employing a natural decomposition method association with newly established Atangana-Baleanu derivative and Caputo-Fabrizio fractional order. The equation considered classical super-extension system. This nonlinear model scheme commonly used to describe waves traffic flow, electromagnetism, electrodynamics, elastic media, multi-component...

In this study, numerical results of a fractional-order multi-dimensional model the Navier–Stokes equations will be achieved via adoption two analytical methods, i.e., Adomian decomposition transform method and q-Homotopy analysis method. The Caputo–Fabrizio operator used to define fractional derivative. proposed methods implemented provide series form given models. techniques validated with exact available in literature. investigated efficient, straightforward, reliable for application many...

In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find solution nonlinear fractional Gardner and Cahn–Hilliard equations arising in fluid flow. The derivative is considered an Atangana–Baleanu Caputo manner (ABC) Caputo–Fabrizio (CF) throughout paper. We implement transform aid of suggested obtain followed by inverse transform. To show accuracy validity proposed methods, focused on two problems compared it exact other method results....

<abstract><p>This article shows how to solve the time-fractional Fisher's equation through use of two well-known analytical methods. The techniques we propose are a modified form Adomian decomposition method and homotopy perturbation with Yang transform. To show accuracy suggested techniques, illustrative examples considered. It is confirmed that solution get by implementing has desired rate convergence towards accurate solution. main benefit proposed small number calculations....

In this article, we investigate the nonlinear model describing various physical and chemical phenomena named Kuramoto–Sivashinsky equation. We implemented natural decomposition method, a novel technique, mixed with Caputo–Fabrizio (CF) Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining approximate analytical solution of equation (FKS). The proposed method gives series form which converges quickly towards exact solution. To show accuracy examine three...

<abstract><p>In this paper, we used the Natural decomposition approach with nonsingular kernel derivatives to explore modified Boussinesq and approximate long wave equations. These equations are crucial in defining features of shallow water waves using a specific dispersion relationship. In research, convergence analysis error have been provided. The fractional Atangana-Baleanu Caputo-Fabrizio utilised throughout paper. To obtain results, transform on fractional-order equations,...

This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The coupled systems investigated in this current analysis are applied as model physical phenomena arising chemistry, biology, physics, sciences. Approximate analytical results represented form series straightforward components, some aspects showed an appropriate...

In this work, the novel iterative transformation technique and homotopy perturbation are used to calculate fractional-order gas dynamics equation. technique, iteration method combined with Elzaki transformation. The current methods implemented four examples show efficacy validation of techniques. approximate solutions obtained by given techniques that accurate easy apply other linear nonlinear problems.

Partially ionised fluids subject to an external magnetic field results in a completely different dynamical behaviour. Very few studies are conducted explore the fascinating properties of Hall current and Ion slip fluid flows. Flow over Riga plate with MHD currents, nonlinear thermal radiation is still rare. We aim analyse inclined stagnation point flow Couple Stress stretched horizontal close this gap. The problem modelled using Navier stokes theory along energy conservation then principal...

Abstract The area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. search traveling wave solutions is a difficult task, which led the creation numerous mathematical approaches tackle this problem. primary objective research work provide optical soliton Frictional Kundu–Eckhaus equation (FKEe) by utilizing generalized coefficients. This strategy utilizes Riccati–Bernoulli sub-ODE technique effectively...