Analysis and numerical computations of the fractional regularized long‐wave equation with damping term. (19th March 2020)

• Record Type: Journal Article
• Authors: Yavuz, Mehmet; Sulaiman, Tukur Abdulkadir; Usta, Fuat; Bulut, Hasan
• Other Names: Tosun Murat guestEditor.; Kara Emrah Evren guestEditor.; Usta Fuat guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 9(2021)
• Page Start: 7538
• Page End: 7555
• Publication Date: 2020-03-19
• Subjects: Atangana‐Baleanu derivative -- Caputo derivative -- Caputo‐Fabrizio derivative -- existence -- nonlinear waves -- uniqueness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6343
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we show the existence and uniqueness of the solution to the damped generalized regularized long‐wave equation. The modified Laplace decomposition method (MLDM) defined in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio (in the Riemann sense) operators is used in securing the approximate‐analytical solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed with different suitable values of ρ, which is the order of fractional parameter. We have seen the effect of the various parameters and variables on the displacement in figures.