Solving a system of nonlinear fractional differential equations using Adomian decomposition

By Hossein Jafari, Varsha Daftardar-Gejji. 2006

242 citations recorded by the source corpus.

Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: Dxiyi(x) = Ni(x, y1,...,yn), yi(k)(0) = cki, 0 ≤k ≤[αi], 1≤i≤n and Dxi denotes Caputo fractional derivative.Some examples are solved as illustrations, using symbolic computation.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e4bebb29e8e6f948253431a4f5da9ae79ec48835

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Citations in the corpus

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials (2012, methodology): “[9] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Solutions of the fractional Davey-Stewartson equations with variational iteration method.”
Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation (2015, unknown): “, the finite difference method [11,12], reproducing kernel space method [13,14], Adams–Bashforth–Moulton method [15], homotopy perturbation method [16,17], Adomian decomposition method [18,19], homotopy analysis method [20,21], and generalized differential transform method [22,23].”
Positive solutions of a boundary value problem for a nonlinear fractional differential equation. (2008, unknown): “While much attention has focused on the Cauchy problem for fractional differential equations for both the Reimann-Liouville and Caputo differential operators, see [8, 17, 24, 28, 29, 30, 31, 32, 34] and references therein, there are few papers devoted to the study of fractional order boundary value ”
Solving systems of fractional differential equations using differential transform method (2008, result): “4 and 5 are in very good agreement with the results obtained in [7] using the Adomian decomposition method.”
Solving a fourth‐order fractional diffusion‐wave equation in a bounded domain by decomposition method (2008, methodology): “Ginoa et al. [8] have presented a fractional diffusion equation describing relaxation Correspondence to: Hossein Jafari, Department of Mathematics and Computer Science, University of Mazandaran, Babolsar, Iran (e-mail: jafari_h@math.com) © 2007 Wiley Periodicals, Inc. phenomena in complex viscoelast”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[164] H.”