IJAAMM Int. J. Adv. Appl. Math. and Mech. 6(3) (2019) 1 – 13 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics New modification of Adomian decomposition method for solving a system of nonlinear fractional partial differential equations Research Article Hayman Thabet ∗ , Subhash Kendre Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India Received 25 August 2017; accepted (in revised version) 20 February 2019 Abstract: In this paper, we introduce a new modification of Adomian decomposition method (ADM) for solving a system of non- linear fractional partial differential equations (NFPDEs). This modification has been constructed for a general system of NFPDEs, and it is easy to implement numerically. Therefore, this modification is more practical and helpful for solving abroad systems of NFPDEs.The approximate solution for systems of NFPDEs is easily obtained by the means of Caputo fractional partial derivative based on the properties of fractional calculus. Moreover, the convergence and error analysis of the proposed modification are shown. The approximate and numerical solutions for well-known ex- amples are presented in forms of tables and graphs to make a comparison with the results that previously obtained by some other well-known methods. Numerical results are carried out to confirm the accuracy and efficiency of the proposed modification. MSC: 35M31 • 35R11 Keywords: System of nonlinear fractional partial differential equations • Adomian decomposition method • Existence theorem • Error analysis • Approximate solutions © 2019 The Author(s). This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/). 1. Introduction During last few decades, fractional order partial differential equations have been proposed and investigated in many research fields, such as fluid mechanics, mechanics of materials, biology, plasma physics, finance and chem- istry, see [1–6]. The systems of fractional partial differential equations have been increasingly used to represent phys- ical and control systems (see for instant, [7–11] and some references cited therein). Since some of the fractional order partial differential equations do not have exact analytic solutions, approximating or numerical techniques are gener- ally applied. There are many different analytical and numerical methods such as ADM [12], the fractional complex transformation (Elsayed M.E. Zayed ([13]), homotopy perturbation method (S. Momani [14]), a homotopy perturba- tion technique (S. T. Mohyud-Din [15]), Variational iteration method (Z. Odibat [16]), homotopy perturbation trans- form method (Brajesh Kumar Singh and Pramod Kumar [17]), generalized differential transform method (A. Ebadian et al. [18]), decomposition method (Zaid Odibat [16]), Modified least squares homotopy perturbation method (H. Thabet and S. Kendre [19]) and so on. The ADM due to Adomian [20] has been successfully used in solving a wide variety of deterministic as well as stochastic problems in differential equations. The ADM provides the solution in a rapidly convergent series with eas- ily computable components. The main advantage of ADM is that it can be used directly to solve,all types of differential ∗ Corresponding author. E-mail address(es): haymanthabet@gmail.com (Hayman Thabet), sdkendre@yahoo.com (Subhash Kendre).