Approximate solutions of fractional nonlinear equations using homotopy perturbation transformation method

DOI10.1155/2012/752869zbMath1242.65136OpenAlexW2047294146WikidataQ58696736 ScholiaQ58696736MaRDI QIDQ417185

Yanqin Liu

Publication date: 14 May 2012

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/752869

zbMATH Keywords

Laplace transformconvergencenumerical examplesfractional nonlinear equationhomotopy perturbation transformation method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Numerical methods for initial value problems involving ordinary differential equations (65L05) Laplace transform (44A10) Numerical methods for ordinary differential equations (65L99) Fractional ordinary differential equations (34A08)

Related Items (13)

Stability approach to the fractional variational iteration method used for the dynamic analysis of viscoelastic beams ⋮ A comparative study on the analytic solutions of fractional coupled sine-Gordon equations by using two reliable methods ⋮ Fractional calculus for nanoscale flow and heat transfer ⋮ Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions ⋮ Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative ⋮ Unnamed Item ⋮ A tutorial review on fractal spacetime and fractional calculus ⋮ Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order ⋮ Comparison of two reliable analytical methods based on the solutions of fractional coupled Klein-Gordon-Zakharov equations in plasma physics ⋮ Numerical solutions of fractional Fokker-Planck equations using iterative Laplace transform method ⋮ Laplace transform-homotopy perturbation method with arbitrary initial approximation and residual error cancelation ⋮ Variational approximate solutions of fractional nonlinear nonhomogeneous equations with Laplace transform ⋮ Solutions of fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov equations using a generalized fractional subequation method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy perturbation method for nonlinear partial differential equations of fractional order
• On the coupling of the homotopy perturbation method and Laplace transformation
• Homotopy perturbation transform method for nonlinear equations using He's polynomials
• Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
• Beyond Adomian polynomials: He polynomials
• Application of generalized differential transform method to multi-order fractional differential equations
• Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
• Axial couette flow of two kinds of fractional viscoelastic fluids in an annulus
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Recent development of the homotopy perturbation method
• Solutions of a fractional oscillator by using differential transform method
• Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition
• The variational iteration method for analytic treatment for linear and nonlinear ODEs
• Exact solutions for a generalized nonlinear fractional Fokker-Planck equation
• A review of the decomposition method in applied mathematics
• A new modification of the Adomian decomposition method for linear and nonlinear operators
• Application of homotopy perturbation method to nonlinear wave equations
• Numerical solution of Duffing equation by the Laplace decomposition algorithm
• Application of the homotopy perturbation method for the Fokker-Planck equation
• TRAVELING WAVE SOLUTIONS OF SEVENTH-ORDER GENERALIZED KdV EQUATIONS BY VARIATIONAL ITERATION METHOD USING ADOMIAN'S POLYNOMIALS
• Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
• Linear Multistep Methods for the Efficient Integration of the Schrödinger Equation
• Some iterative methods for solving nonlinear equations using homotopy perturbation method
• Exact Solutions of a Generalized Multi-Fractional Nonlinear Diffusion Equation in Radical Symmetry
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Approximate solutions of fractional nonlinear equations using homotopy perturbation transformation method