Numerical Approaches of the Generalized Time-Fractional Burgers' Equation with Time-Variable Coefficients. (8th December 2021)

• Record Type: Journal Article
• Authors: Vieru, Dumitru; Fetecau, Constantin; Shah, Nehad Ali; Chung, Jae Dong
• Other Names: Vetro Calogero Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-12-08
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/8803182
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular cases the Burgers equation with Atangana-Baleanu, Caputo-Fabrizio, and Caputo time-fractional derivatives. A numerical scheme, based on the finite-difference approximations and some integral representations of the two-parameter Mittag-Leffler functions, has been developed. Numerical solutions of a particular problem with initial and boundary values are determined by employing the proposed method. The numerical results are plotted to compare solutions corresponding to the problems with time-fractional derivatives with different kernels.