### AIMS Mathematics

2021, Issue 9: 10055-10069. doi: 10.3934/math.2021584
Research article Special Issues

# Computation of traveling wave solution for nonlinear variable-order fractional model of modified equal width equation

• Received: 06 April 2021 Accepted: 28 June 2021 Published: 07 July 2021
• MSC : 35C07, 35C08, 35K05, 35P99

• The Variable-order fractional operators (VO-FO) have considered mathematically formalized recently. The opportunity of verbalizing evolutionary leading equations has led to the effective application to the modeling of composite physical problems ranging from mechanics to transport processes, to control theory, to biology. In this paper, find the closed form traveling wave solutions for nonlinear variable-order fractional evolution equations reveal in all fields of sciences and engineering. The variable-order evolution equation is an impressive mathematical model describes the complex dynamical problems. Here, we discuss space-time variable-order fractional modified equal width equation (MEWE) and used exp $(-\phi(\xi))$ method in the sense of Caputo fractional-order derivative. Based on variable order derivative and traveling wave transformation convert equation into nonlinear ordinary differential equation (ODE). As a result, constructed new exact solutions for nonlinear space-time variable-order fractional MEWE. It clearly shows that the nonlinear variable-order evolution equations are somewhat natural and efficient in mathematical physics.

Citation: Umair Ali, Sanaullah Mastoi, Wan Ainun Mior Othman, Mostafa M. A Khater, Muhammad Sohail. Computation of traveling wave solution for nonlinear variable-order fractional model of modified equal width equation[J]. AIMS Mathematics, 2021, 6(9): 10055-10069. doi: 10.3934/math.2021584

### Related Papers:

• The Variable-order fractional operators (VO-FO) have considered mathematically formalized recently. The opportunity of verbalizing evolutionary leading equations has led to the effective application to the modeling of composite physical problems ranging from mechanics to transport processes, to control theory, to biology. In this paper, find the closed form traveling wave solutions for nonlinear variable-order fractional evolution equations reveal in all fields of sciences and engineering. The variable-order evolution equation is an impressive mathematical model describes the complex dynamical problems. Here, we discuss space-time variable-order fractional modified equal width equation (MEWE) and used exp $(-\phi(\xi))$ method in the sense of Caputo fractional-order derivative. Based on variable order derivative and traveling wave transformation convert equation into nonlinear ordinary differential equation (ODE). As a result, constructed new exact solutions for nonlinear space-time variable-order fractional MEWE. It clearly shows that the nonlinear variable-order evolution equations are somewhat natural and efficient in mathematical physics.

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