Solving a system of nonlinear fractional differential equations using Adomian decomposition

Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

“…The Adomian decomposition method [4], variational iteration method [5], homotopy perturbation method [6] and predictor-corrector method [7] are some of the more famous methods. In particular, systems of FDEs are considered in [8] where the Adomian decomposition method was employed for the solutions of system of nonlinear fractional differential equations. In [9] the homotopy analysis method (HAM) was used for the solutions of a system of nonlinear fractional partial differential equations, while in [10], a modification of Adomian decomposition method was introduced and used for solving a system of nonlinear equations, which produce a series solution with accelerated convergence.…”

An Algorithm for the Approximation of Fractional Differential-Algebraic Equations with Caputo-type Derivatives

“…This has further generated further and more intense interest in finding numerical methods which accurately and efficiently solve nonlinear fractional differential equations. Some of the methods include Adomian Decomposition Method (ADM) [7][8][9][10][11][12][13], the Variational Iteration Method (VIM) [13][14][15][16], Homotopy Analysis Method (HAM) [17][18][19], Homotopy perturbation Method (HPM) [13,20]. Many physical problems are governed by a system of differential-Algebraic Equations (DAE's), and the solution of these equations has been a subject of many investigations in recent years [7][8][9][14][15][16]18,19,21,22].…”

“…In [17,19], the Homotopy Analysis Method (HAM) was applied for Fractional Differential-Algebraic Equations (FDAE's). The Adomian Decomposition Method (ADM) was applied in [7,[9][10][11]20,23] while in [16] the Variational Iteration Method was applied and the Differential Transform was applied in [14,21].…”

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

“…[2,21] and the references therein). Daftardar-Gejji and Jafari [4,7] have employed the Adomian c 2013 Diogenes Co., Sofia pp. 109-122 , DOI: 10.2478/s13540-013-0008-9 decomposition method to solve the linear/nonlinear systems of fractional differential equations which gives numerical answers to any order of desired accuracy.…”