Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations. (November 2018)

• Record Type: Journal Article
• Authors: Yusuf, Abdullahi; Inc, Mustafa; Isa Aliyu, Aliyu; Baleanu, Dumitru
• Is Part Of: Chaos, solitons and fractals. Volume 116(2018)
• Page Start: 220
• Page End: 226
• Publication Date: 2018-11
• Subjects: Fractional RHE -- Fractional CmKdV -- AB derivative -- CF -- FHPTM -- Numerical simulations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.09.036
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Some nonlinear partial differential equations with new fractional derivative are investigated. The existence and uniqueness analysis of the solution are reported. The numerical results are obtained by using an iterative method. Efficincy of Atangana–Baleanu fractional derivative over well known Caputo–Fabrizio fractional derivative is illustrated. Abstract: In this work, the efficiency of the Atangana–Baleanu (AB) derivative over Caputo–Fabrizio (CF) to some nonlinear partial differential equation is presented. The considered equations are Rosenou–Haynam equation (RHE) and a class of mKdV (CmKdV) equation. The effective and efficient technique called the fractional homotopy perturbation transform method (FHPTM) is applied for the investigation of the governing equations.