Fractional dynamics study: analytical solutions of modified Kordeweg-de Vries equation and coupled Burger’s equations using Aboodh transform

Scientific Reports, Journal Year: 2024, Volume and Issue: 14(1)

Published: June 3, 2024

Abstract The study examines the using of Aboodh residual power series method and transform iteration (ATIM) to analyze modified Korteweg-de Vries equation (mKdV) beside coupled Burger’s equations in framework Caputo operator. These sets represent non-linear wave description for various physical systems. Through APM ATIM, solution mKdV get accurate dynamics information that will reveal nature their interactions. Using mathematically proven techniques computational simulations, developed methods’ efficiency reliability are illustrated complex behaviors these nonlinear equations, so we can gain deeper insights into dynamics. research is aimed at an increase knowledge about fractional calculus utilization motion it also provides analytical tools analysis acting different scientific engineering areas.

Language: Английский

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An effective extended cubic B-spline approach for solving time-fractional diffusion wave equation with exponential kernel

Alexandria Engineering Journal, Journal Year: 2025, Volume and Issue: 117, P. 148 - 163

Published: Jan. 13, 2025

Language: Английский

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Analytical solution of the systems of nonlinear fractional partial differential equations using conformable Laplace transform iterative method

AIMS Mathematics, Journal Year: 2025, Volume and Issue: 10(2), P. 1945 - 1966

Published: Jan. 1, 2025

<p>In this study, we presented the conformable Laplace transform iterative method to find approximate solution of systems nonlinear temporal-fractional differential equations in sense derivative. The advantage suggested approach was compute without discretization and restrictive assumptions. Three distinct examples were provided show applicability efficacy proposed approach. To examine exact solutions, utilized 2D 3D graphics. Furthermore, outcomes produced study consistent with solutions; hence, strategy efficiently effectively determined solutions equations.</p>

Language: Английский

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Abundant Elliptic, Trigonometric, and Hyperbolic Stochastic Solutions for the Stochastic Wu–Zhang System in Quantum Mechanics

Mathematics, Journal Year: 2025, Volume and Issue: 13(5), P. 714 - 714

Published: Feb. 22, 2025

In this article, we look at the stochastic Wu–Zhang system (SWZS) forced by multiplicative Brownian motion in Itô sense. The mapping method, which is an effective analytical employed to investigate exact wave solutions of aforementioned equation. proposed scheme provides new types including periodic solitons, kink singular solitons and so on, describe propagation quantum mechanics analyze a wide range essential physical phenomena. absence noise, obtain some previously found SWZS. Additionally, using MATLAB program, impacts noise term on solution SWZS were demonstrated.

Language: Английский

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Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique

Open Physics, Journal Year: 2025, Volume and Issue: 23(1)

Published: Jan. 1, 2025

Abstract In this article, we study the time-dependent two-dimensional system of Wu–Zhang equations fractional order in terms Caputo operator, which describes long dispersive waves that minimize and analyze damaging effects caused by these waves. This article centers on finding soliton solutions a non-linear ( 2 + 1 2+1 )-dimensional time-fractional system, has become significant point interest for its ability to describe dynamics gravity water The semi-analytical method called q q -homotopy analysis amalgamation with Laplace transform is applied uncover an analytical solution equations. outcomes obtained through considered are form series solution, they converge swiftly. results coincide exact portrayed graphs carried out numerical simulations shows minimum residual error. technique used here reliable well organized, enhances analyzing higher-dimensional differential various sectors science engineering.

Language: Английский

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An innovative approach to approximating solutions of fractional partial differential equations

Physica Scripta, Journal Year: 2024, Volume and Issue: 99(6), P. 065259 - 065259

Published: May 9, 2024

Abstract The RPS-M (residual power series method) is a valuable technique for solving F-PDEs (fractional partial differential equations). However, the derivative of residual function to obtain coefficients required in RPS-M. This makes application classical limited certain extent due complexity derivation higher iterations. To overcome this obstacle, study, we present simplified version approach with help Laplace transform that requires less computation and offers accuracy. modified method does not require as well limit estimate unknown solution. demonstrate its effectiveness, apply proposed nonlinear their semi-analytical obtained solutions exhibit excellent agreement when compared results using other established approaches. We have also provided convergence analysis Furthermore, by comparing outcomes various values non-integer order σ , observe value approaches an integer order, solution converges towards exact

Language: Английский

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Efficient solutions for time fractional Sawada-Kotera, Ito, and Kaup-Kupershmidt equations using an analytical technique

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(8), P. 20441 - 20466

Published: Jan. 1, 2024

<abstract><p>We focused on the analytical solution of strong nonlinearity and complicated time-fractional evolution equations, including Sawada-Kotera equation, Ito Kaup-Kupershmidt using an effective accurate method known as Aboodh residual power series (ARPSM) in framework Caputo operator. Therefore, operator ARPSM are practical for figuring out a linear or nonlinear system with fractional derivative. This technique was effectively proposed to obtain set solutions various types differential equations. The derived enabled us understand mechanisms behind propagation generation numerous phenomena observed diverse scientific domains, plasma physics, fluid optical fibers. property also revealed some ambiguity that may be many natural phenomena, this is one most important distinguishing factors between equations non-fractional ones. We helped clarify calculus dynamics, motivating researchers work mathematical physics.</p></abstract>

Language: Английский

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Analytical investigation of convective phenomena with nonlinearity characteristics in nanostratified liquid film above an inclined extended sheet

Nanotechnology Reviews, Journal Year: 2024, Volume and Issue: 13(1)

Published: Jan. 1, 2024

Abstract This work focuses on the time-variant convective thin-film nanoliquid fluid flow and heat transfer over a stretching, inclined surface under effect of magnetism for different energy technologies sustainability. It is crucial to understand how solid materials can be treated with thin films while focusing actual ability improve body features infiltration, shock resistance, rigidness, brightness, dispersal, absorption, or electrical efficiency. All these improvements are invaluable, especially in field nanotechnology. As any mass thermal transport phenomena, study breaks down important factors such as thermophoresis Brownian movement, an attempt energetic balance lessen fuel consumption. Utilizing mathematical model temporal evolution liquid film characteristics surface, we obtain system nonlinear partial differential equations convert it coupled ordinary appropriately. Finally, results problem computational analysis produced using Laplace Adomian decomposition method (LADM) shown both quantitatively visually. During analysis, impact specific parameters magnetic, Brownian, examined found highly significant. Furthermore, that effects ( M M ) (Nt) F F ), Φ \Phi ϕ \phi lead decreased conduction. Conversely, gradient within rises proportion (Nb) factor. research distinguished from similar attempts made past terms planes application LADM approach toward modeling. The findings have provided tangible use coming up new methods cooling electronics gadgets, harvesting solar energy, eco-friendly industrial processes.

Language: Английский

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Fractional view analysis of coupled Whitham- Broer-Kaup and Jaulent-Miodek equations

Ain Shams Engineering Journal, Journal Year: 2024, Volume and Issue: 15(8), P. 102830 - 102830

Published: May 1, 2024

In this study, I systematically investigate the fractional Whitham-Broer-Kaup (WBK) system and Coupled Jaulent-Miodek (CJM) equation under Caputo calculus. The nonlinear differential systems are investigated via Aboodh transform iteration method residual power series method, thus offering a thorough analytical investigation. dynamics of WBK accomplished using is employed to study behavior CJM equation. Using established solutions, we completely analyze their employing both symbolic computations numerical simulations. Consequently, novel solutions identified, these in operator sense clarified. results obtained show good agreement convergence highlighting effectiveness schemes adopted for unraveling complex systems.

Language: Английский

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Fractional view analytical analysis of generalized regularized long wave equation

Open Physics, Journal Year: 2024, Volume and Issue: 22(1)

Published: Jan. 1, 2024

Abstract In this research study, we focus on the generalized regularized long wave equation and modified equation, which play pivotal roles in characterizing plasma waves oceans ion acoustic shallow water, a domain deeply rooted physical phenomena. Employing two computational techniques, namely, optimal auxiliary function method Laplace iterative transform method, approximate these equations. These formulas are used to characterize water. The results discovered have important ramifications for our comprehension of many events. Our show that both methods robust, easy use, successful. Both yield satisfactory each other. With use tables graphs, compared suggested approaches. findings suggest can be widely applied explore other real-world problems.

Language: Английский

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