Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients

Abstract

In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.

Keywords

• nonlinear time-fractional wave-like equations
• caputo fractional derivative
• fractional natural decomposition method
• adomian polynomials
• 35r11
• 34k28
• 26a33
• 35a22