Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation

DOI10.1016/j.camwa.2010.09.009zbMath1219.65144OpenAlexW2140586964MaRDI QIDQ636659

Muhammad Ayaz, Najeeb Alam Khan, Nasir-Uddin Khan, Amir Mahmood

Publication date: 28 August 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.09.009

zbMATH Keywords

analytical solutiondifferential transform method (DTM)homotopy perturbation method (HPM)fractional differential equations (FDE)Swift-Hohenberg (S-H) equation

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Viscoelastic fluids (76A10) Numerical methods for partial differential equations, boundary value problems (65N99) Fractional partial differential equations (35R11)

Related Items (12)

The analytical analysis of nonlinear fractional-order dynamical models ⋮ An iterative method for time-fractional Swift-Hohenberg equation ⋮ APPROXIMATE SOLUTIONS OF THE SWIFT-HOHENBERG EQUATION WITH DISPERSION ⋮ A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations ⋮ An efficient approach for solving the Riccati equation with fractional orders ⋮ The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet ⋮ Optimal variational asymptotic method for nonlinear fractional partial differential equations ⋮ Application of homotopy analysis method for fractional Swift Hohenberg equation -- revisited ⋮ On efficient method for system of fractional differential equations ⋮ Rational spline-nonstandard finite difference scheme for the solution of time-fractional Swift-Hohenberg equation ⋮ Numerical solutions to the time-fractional Swift-Hohenberg equation using reproducing kernel Hilbert space method ⋮ Application of the dual reciprocity boundary integral equation approach to solve fourth-order time-fractional partial differential equations

Cites Work

• Unnamed Item
• Analytical and numerical results for the Swift-Hohenberg equation
• Modified Adomian polynomials
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Evidence for slow velocity relaxation in front propagation in Rayleigh-Bénard convection
• Homotopy perturbation method: a new nonlinear analytical technique
• Pattern selection of solutions of the Swift--Hohenberg equation
• Generalized differential transform method: Application to differential equations of fractional order
• Recent Developments in Rayleigh-Bénard Convection

This page was built for publication: Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation