Solution of system of fractional differential equations by Adomian decomposition method

Abstract

The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffler functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.

Numerical method for fractional dispersive partial differential equations

“…In order to attain the aim of extremely accuracy and consistent solutions, numerous approaches have been suggested to crack the fractional order differential equations. Some of the current analytical/numerical methods are Adomian decomposition method (ADM) [15][16][17][18][19][20], finite difference method [21], Operational matrix method [22], Homotopy analysis method [23,-24], generalized differential transform method [25,26], finite element method [27], fractional differential transform method [28][29] and references therein. http://www.ispacs.com/journals/cna/2017/cna-00266/ International Scientific Publications and Consulting Services…”

A generalization of the Mittag–Leffler function and solution of system of fractional differential equations

“…From Eqs. (39), (40) and (41), the analytic approximate solutions y [14] 1 (t), y [14] 2 (t) and y [14] 3 (t) are calculated using the approximations of the first 14 terms, G [14] (t) and Q [14] (t). The numeric solutions y 1,i , y 2,i and y 3,i for i = 1, 2, .…”

“…Daftardar-Gejji and Babakhani [37] and Deng et al [38] studied the existence, uniqueness and stability for solution of system of linear fractional differential equations with constant coefficients. Other references include [39][40][41]. In the above literature, solutions of the fractional differential system were given for the case of a commensurate order system.…”

A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations

“…Most systems of fractional integrodifferential equations do not have exact solutions, so numerical techniques are used to solve such systems. The homotopy perturbation method, the Adomian decomposition method, and other methods are used to give an approximate solution to linear and nonlinear problems; see [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”