A behavioral analysis of KdVB equation under the law of Mittag–Leffler function
| Autor: | M. Khumalo, H.M. Tenkam, Emile Franc Doungmo Goufo |
|---|---|
| Přispěvatelé: | 33251657 - Tenkam, Herve Michel |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
General Physics and Astronomy Parameterized complexity Perturbation (astronomy) Existence Mittag–Leffler Kernel 01 natural sciences 010305 fluids & plasmas symbols.namesake Mittag-Leffler function 0103 physical sciences Fluid dynamics Applied mathematics Uniqueness 010301 acoustics Wave dynamics Mathematics Fundamental theorem Applied Mathematics Statistical and Nonlinear Physics Uniquenes Fractional model Fractional calculus Burgers' equation KdVB-equation symbols |
| Zdroj: | Chaos, Solitons & Fractals. 125:139-145 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2019.05.020 |
| Popis: | The literature on fluid dynamics shows that there still exist number of unusual irregularities observed in wave motions described by the Korteweg–de Vries equation, Burgers equation or the combination of both, called Korteweg–de Vries–Burgers (KdVB) equation. In order to widen the studies in the topic and bring more clearness in the wave dynamics, we extend and analyze the KdVB-equation with two levels of perturbation. We combine the model with one of the fractional derivatives with Mittag–Leffler Kernel, namely the Caputo sense derivative with non-singular and non-local kernel (known as ABC-derivative (Atangana–Beleanu–Caputo)). After a brief look at the dynamics of standard integer KdVB-equation, we analyze the combined fractional KdVB-equation by showing its existence and uniqueness results. Numerical simulations using the fundamental theorem of fractional calculus show that the dynamics for the combined model is similar to the integer order dynamics, but highly parameterized and controlled by the order of the fractional derivative with Mittag–Leffler Kernel. |
| Databáze: | OpenAIRE |
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