Application of the Caputo-Fabrizio Fractional Derivative without Singular Kernel to Korteweg-de Vries-Burgers Equation*. Issue 2 (3rd March 2016)

• Record Type: Journal Article
• Authors: Doungmo Goufo, Emile Franc
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 2(2016)
• Page Start: 188
• Page End: 198
• Publication Date: 2016-03-03
• Subjects: Caputo-Fabrizio fractional derivative -- non-linear Korteweg-de Vries-Burgers equation -- existence and uniqueness -- perturbation -- numerical solutions; 26A33 -- 34A12 -- 35D05; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1145607
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: In order to bring a broader outlook on some unusual irregularities observed in wave motions and liquids' movements, we explore the possibility of extending the analysis of Korteweg–de Vries–Burgers equation with two perturbation's levels to the concepts of fractional differentiation with no singularity. We make use of the newly developed Caputo-Fabrizio fractional derivative with no singular kernel to establish the model. For existence and uniqueness of the continuous solution to the model, conditions on the perturbation parameters ν, μ and the derivative order α are provided. Numerical approximations are performed for some values of the perturbation parameters. This shows similar behaviors of the solution for close values of the fractional order α .