New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations

Abstract

This paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is shown. The approximate solutions for a system of NFPDEs are easily obtained by means of Caputo fractional partial derivatives based on the properties of fractional calculus. However, analytical and numerical traveling wave solutions for some systems of nonlinear wave equations are successfully obtained to confirm the accuracy and efficiency of the proposed technique. Several numerical results are presented in the format of tables and graphs to make a comparison with results previously obtained by other well-known methods Keywords: system of nonlinear fractional partial differential equations (NFPDEs); systems of nonlinear wave equations; new analytical technique (NAT); existence theorem; error analysis; approximate solution

Travelling wave solution of Dodd-Bullough-Mikhailov equation: a comparative study between Generalized Kudryashov and improved F-expansion methods

“…For example, F-expansion method [1,2], tanh-function method [3,4], the Kudrayshov method [5,6], the modified simple equation method [7][8][9], the Jacobi elliptic-function method [10], the Bernoulli sub-ODE method [11,12], the Expfunction method [13,14], the multiple Exp-function method [15,16], the ¢ ( ) / G G -expansion method [17,18], the variational iteration method [19], the homotopy perturbation method [20], the exp f x -( ( ))-expansion method [21], the homotopy analysis method [22,23], the extended tanh-method [24][25][26], the enhanced ¢ ( ) / G G -expansion method [27][28][29], the Generalized Kudryashov method [30][31][32], and the improved F-expansion method [33][34][35][36], to name a few. Few other methods have been proposed in recent years, for example, Shehu transform [37], Caputo fractional partial derivatives [38] and local fractional homotopy analysis method [39]. These methods allow to construct the travelling wave solutions of NLPDEs, which happen to be the remarkable achievements in the field of applied sciences and hence has drawn attraction of many researchers around the world.…”

Correction: Thabet, H.; Kendre, S.; Chalishajar, D. New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations Mathematics 2017, 5, 47

“…We have found some errors in the caption of Figure 1 and Figure 2 in our paper [1], and thus would like to make the following corrections:…”

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We have found some errors in the caption of Figure 1 and Figure 2 in our paper [1], and thus would like to make the following corrections:On page 10, the caption of Figure 1 should be changed from: The authors apologize for any inconvenience caused to the readers. The change does not affect the scientific results.

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Operators of Fractional Calculus and Their Applications

“…Website: http://www.math.uvic.ca/faculty/harimsri/ This volume contains the successfully invited and accepted submissions (see [1][2][3][4][5][6][7][8][9]) to a Special Issue of MDPI's journal, Mathematics in the subject area of "Operators of Fractional Calculus and Their Applications".…”