Journal
MATHEMATICAL MODELLING AND ANALYSIS
Volume 21, Issue 2, Pages 188-198Publisher
VILNIUS GEDIMINAS TECH UNIV
DOI: 10.3846/13926292.2016.1145607
Keywords
existence and uniqueness; Caputo-Fabrizio fractional derivative; non-linear Korteweg-de Vries-Bergers equation; numerical solutions; perturbation; 34A12; 26A33; 35D05
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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-Bergers 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 nu, mu and the derivative order alpha 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 alpha.
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