Application of the Caputo-Fabrizio Fractional Derivative without Singular Kernel to Korteweg-de Vries-Burgers Equation

• Published in: Mathematical modelling and analysis Vol. 21; no. 2; pp. 188 - 198
• Main Author: Doungmo Goufo, Emile Franc
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 18.03.2016; Vilnius Gediminas Technical University
• Subjects: Caputo-Fabrizio fractional derivative; Derivatives (Mathematics); Equations (Mathematics); existence and uniqueness; Kernel functions; Mathematical research; non-linear Korteweg-de Vries-Burgers equation; numerical solutions; perturbation; Perturbation theory; non-linear Korteweg-de Vries-Burgers equation; numerical solutions; existence and uniqueness; perturbation; Caputo-Fabrizio fractional derivative
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2016.1145607

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.