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

• Main Authors: Khalouta Ali, Kadem Abdelouahab
• Format: Article
• Language: English
• Published: Sciendo 2019-08-01
• Series: Acta Universitatis Sapientiae: Mathematica
• Subjects: nonlinear time-fractional wave-like equations; caputo fractional derivative; fractional natural decomposition method; adomian polynomials; 35r11; 34k28; 26a33; 35a22
• Online Access: https://doi.org/10.2478/ausm-2019-0009

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.