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