Analytical study for time and time-space fractional Burgers’ equation

• Published in: Advances in difference equations Vol. 2017; no. 1; pp. 1 - 15
• Main Authors: Saad, KM, Al-Sharif, Eman HF
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 26-09-2017; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Burgers equation; Difference and Functional Equations; different initial values; Exact solutions; Functional Analysis; Initial conditions; Iterative methods; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; space-time fractional Burgers equation; variational iteration method; space-time fractional Burgers equation; different initial values; variational iteration method
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-017-1358-0

In this paper, the variational iteration method (VIM) is applied to solve the time and space-time fractional Burgers’ equation for various initial conditions. VIM solutions are computed for the fractional Burgers’ equation to show the behavior of VIM solutions as the fractional derivative parameter is changed. The results obtained by VIM are compared with exact solutions and also with expansions of the exact solutions. VIM solutions are found to be in excellent agreement with these exact solutions.