Exact solutions of (1+2)-dimensional non-linear time-space fractional PDEs

Abstract

Purpose – In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs). Design/methodology/approach – The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM). Findings – The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations. Originality/value – The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

Keywords

• Caputo derivative
• FPDEs
• Error analysis
• Sumudu transform
• Daftardar-Gejji and Jafari method
• Population model