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

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.

Keywords

• Caputo-Fabrizio fractional derivative
• non-linear Korteweg-de Vries-Burgers equation
• existence and uniqueness
• perturbation
• numerical solutions