Fractional differential transform method combined with the Adomian polynomials

DOI10.1016/j.amc.2011.12.066zbMath1244.65101OpenAlexW2072753577MaRDI QIDQ428105

Ahmed Elsaid

Publication date: 19 June 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.12.066

zbMATH Keywords

numerical examplesnonlinear equationsAdomian polynomialsnonlinear fractional differential equationsfractional differential transform method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Fractional ordinary differential equations (34A08)

Related Items

Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science, On the solution of characteristic value problems arising in linear stability analysis; semi analytical approach, Existence of solutions to nonlinear fractional differential equations with boundary conditions on an infinite interval in Banach spaces, A semi-analytic method with an effect of memory for solving fractional differential equations, Asymptotic Decomposition Method for Fractional Order Riccati Differential Equation, Local fractional Fourier series method for solving nonlinear equations with local fractional operators, Adaptive fuzzy synchronization of fractional-order chaotic (hyperchaotic) systems with input saturation and unknown parameters, An efficient multi-derivative numerical method for chemical boundary value problems, Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel, A constructive approach for solving system of fractional differential equations, Positive solutions of fractional differential equation nonlocal boundary value problems, Unnamed Item, Efficient analytic method for solving nonlinear fractional differential equations, A study of projectile motion in a quadratic resistant medium via fractional differential transform method, An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations, Fractional boundary value problems with Riemann-Liouville fractional derivatives

Cites Work

• Unnamed Item
• An efficient algorithm for the multivariable Adomian polynomials
• Convenient analytic recurrence algorithms for the Adomian polynomials
• Decomposition method for solving fractional Riccati differential equations
• A numerical scheme for the solution of multi-order fractional differential equations
• Generalized Taylor's formula
• Recurrence triangle for Adomian polynomials
• Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions
• Partial differential equations and solitary waves theory
• Solving frontier problems of physics: the decomposition method
• A new algorithm for calculating one-dimensional differential transform of nonlinear functions
• Adomian method for solving some coupled systems of two equations
• Solution of fractional differential equations by using differential transform method
• Toward a new analytical method for solving nonlinear fractional differential equations