Approximate solutions to fractional differential equations

DOI10.1007/s10483-023-3041-9zbMath1528.76027MaRDI QIDQ6084635

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Publication date: 2 December 2023

Published in: AMM. Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

series solutionCaputo fractional derivativehomotopy perturbation methodcoupled viscous Burgers equationDrinfeld-Sokolov-Wilson equationSawi transform

Mathematics Subject Classification ID

Incompressible viscous fluids (76D99) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Fractional derivatives and integrals (26A33)

Cites Work

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• Homotopy perturbation transform method for nonlinear equations using He's polynomials
• Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method
• Modification of the decomposition approach to the heat equation
• Application of the Burgers' equation with a variable coefficient to the study of nonplanar wave transients
• Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solutions of Boussinesq-Burger equations
• Homotopy perturbation method for solving time fractional coupled viscous Burgers' equation in \((2+1)\) and \((3+1)\) dimensions
• New double-periodic solutions of fractional Drinfeld-Sokolov-Wilson equation in shallow water waves
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Homotopy perturbation technique
• A new analysis of fractional Drinfeld-Sokolov-Wilson model with exponential memory
• On numerical doubly periodic wave solutions of the coupled Drinfel'd-Sokolov-Wilson equation by the decomposition method
• Homotopy perturbation method for fractional KdV equation
• Homotopy analysis Sumudu transform method for time-fractional third order dispersive partial differential equation
• Invariant analysis and exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation by Lie group analysis
• A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients
• An efficient numerical method for solving coupled Burgers' equation by combining homotopy perturbation and pade techniques
• Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method
• New soliton solutions of the time fractional Drinfeld–Sokolov–Satsuma–Hirota system in dispersive water waves
• He's variational method for the time–space fractional nonlinear Drinfeld–Sokolov–Wilson system

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