4.6 Article

Approximate solutions to fractional differential equations

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

He's variational method for the time-space fractional nonlinear Drinfeld-Sokolov-Wilson system

Kang-Jia Wang et al.

Summary: This paper investigates the time-space fractional Drinfeld-Sokolov-Wilson system and solves its solitary solutions using He's variational method and the two-scale transform. The applicability and efficiency of the approach are demonstrated through numerical results. The main advantage of the variational approach is its ability to simplify the differential equation.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2023)

Article Mathematics, Applied

Semi-analytical and numerical study of fractal fractional nonlinear system under Caputo fractional derivative

Obaid Algahtani et al.

Summary: This article investigates the fractional Drinfeld-Sokolov-Wilson system with fractal dimensions under the power-law kernel. The integral transform using the Adomian decomposition technique is applied to study the general series solution and the applications of the model with fractal-fractional dimensions. The numerical case with appropriate subsidiary conditions validates the model and provides a detailed numerical/physical interpretation. The results reveal the effects of minimizing the fractal dimension and reducing the fractional order on the solitary wave solution, as well as the behavior of the coupled system.

AIMS MATHEMATICS (2022)

Article Mathematics, Applied

Numerical solutions of time and space fractional coupled Burgers equations using time-space Chebyshev pseudospectral method

Avinash K. Mittal et al.

Summary: The paper introduces a spectrally accurate time-space pseudospectral method for the approximate solution of nonlinear time and space fractional coupled Burgers equations. By using different fractional derivative matrices, simplifying the problem, and transforming nonhomogeneous initial-boundary values through a mapping, highly accurate numerical results are obtained with error analysis presented.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

Article Thermodynamics

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

Muhammad Nadeem et al.

Summary: This study aims to use Mohand transform and homotopy perturbation method to solve the fractional view of Newell-Whitehead-Segel equation, showing that this strategy is simple, smooth, and performs well in agreement with exact solution.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW (2021)

Article Mathematics, Applied

New soliton solutions of the time fractional Drinfeld-Sokolov-Satsuma-Hirota system in dispersive water waves

Santanu Saha Ray et al.

Summary: This paper utilizes the conformable Laplace homotopy perturbation method to solve time fractional coupled Drinfeld-Sokolov-Satsuma-Hirota equations. The excellent agreement of results with other numerical methods demonstrates the reliability and efficiency of the method in solving the considered system.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

Article Physics, Multidisciplinary

A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers' equations in water flow

Muammer Ayata et al.

Summary: In this paper, the conformable Laplace decomposition method (CLDM) is used for the first time in solving time fractional systems of Drinfeld-Sokolov-Wilson equation (DSWE) and coupled viscous Burgers' equation (CVBE). The results show that CLDM is efficient, reliable, easy to apply, and provides a new perspective for solving various nonlinear fractional partial differential equations in physics.

PHYSICA SCRIPTA (2021)

Article Mathematics, Interdisciplinary Applications

Homotopy Perturbation Method for the Fractal Toda Oscillator

Ji-Huan He et al.

Summary: This paper demonstrates the basic properties of a fractal oscillator using fractal variational theory and introduces a new form of the Toda oscillator free of the exponential nonlinear term through the homotopy perturbation method. The analytical solution is validated through numerical tests, showing excellent agreement, and the graphical illustration further elucidates the effect of the order of the fractal derivative on the vibration property.

FRACTAL AND FRACTIONAL (2021)

Article Physics, Multidisciplinary

A new analysis of fractional Drinfeld-Sokolov-Wilson model with exponential memory

Sanjay Bhatter et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2020)

Article Physics, Multidisciplinary

Exact solutions of time-fractional generalised Burgers-Fisher equation using generalised Kudryashov method

Ramya Selvaraj et al.

PRAMANA-JOURNAL OF PHYSICS (2020)

Article Engineering, Multidisciplinary

A powerful approach for fractional Drinfeld-Sokolov-Wilson equation with Mittag-Leffler law

Wei Gao et al.

ALEXANDRIA ENGINEERING JOURNAL (2019)

Article Engineering, Marine

New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves

Orkun Tasbozan et al.

OCEAN ENGINEERING (2018)

Article Mathematics, Applied

Homotopy analysis Sumudu transform method for time-fractional third order dispersive partial differential equation

Rishi Kumar Pandey et al.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2017)

Article Mathematics, Applied

A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients

Ali Bhrawy et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2016)

Article Physics, Multidisciplinary

Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order

S. J. Johnston et al.

OPEN PHYSICS (2016)

Article Engineering, Multidisciplinary

Numerical solution of time- and space-fractional coupled Burgers' equations via homotopy algorithm

Jagdev Singh et al.

ALEXANDRIA ENGINEERING JOURNAL (2016)

Article Mathematics, Applied

Homotopy perturbation transform method for nonlinear equations using He's polynomials

Yasir Khan et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2011)

Article Mathematics, Applied

An Efficient Numerical Method for Solving Coupled Burgers' Equation By Combining Homotopy Perturbation and Pade Techniques

Alev Kelleci et al.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2011)

Article Mathematics, Applied

Homotopy perturbation method for fractional KdV equation

Qi Wang

APPLIED MATHEMATICS AND COMPUTATION (2007)