Solving fuzzy ( 1 + n ) $(1+ n)$ -dimensional Burgers’ equation

• Main Authors: Mawia Osman, Zengtai Gong, Altyeb Mohammed Mustafa, Hong Yang
• Format: Article
• Language: English
• Published: SpringerOpen 2021-04-01
• Series: Advances in Difference Equations
• Subjects: Fuzzy numbers; Fuzzy-valued functions; gH-differentiability; FDTM, FADM, FHPM, and FRDTM; Fuzzy ( 1 + n ) $(1+ n)$ -dimensional Burgers equation
• Online Access: https://doi.org/10.1186/s13662-021-03376-y

Abstract In this paper, we study the comparison of fuzzy differential transform method (FDTM), fuzzy Adomian decomposition method (FADM), fuzzy homotopy perturbation method (FHPM), and fuzzy reduced differential transform method (FRDTM) to obtain the solutions of fuzzy ( 1 + n ) $(1 + n)$ -dimensional Burgers’ equation under gH-differentiability. We have investigated many new results to solve the above problem, and the methods have been implemented. The four illustrative numerical examples are presented to demonstrate the effectiveness of the proposed methods and also to demonstrate the efficiency and simplicity of the ways they were developed and derived. The results also show that the methods are powerful mathematical tools for solving fuzzy ( 1 + n ) $(1 + n)$ -dimensional Burgers’ equation.