Numerical investigation of fractional-order Kersten–Krasil’shchik coupled KdV–mKdV system with Atangana–Baleanu derivative

• Published in: Advances in continuous and discrete models Vol. 2022; no. 1
• Main Authors: Iqbal, Naveed, Botmart, Thongchai, Mohammed, Wael W., Ali, Akbar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 02.05.2022; Springer Nature B.V
• Subjects: Analysis; Difference and Functional Equations; Elastic media; Electrodynamics; Electromagnetism; Functional Analysis; Investigations; Laplace transforms; Mathematics; Mathematics and Statistics; Numerical analysis; Ordinary Differential Equations; Partial Differential Equations; Perturbation; Plasmas (physics); Shallow water; Water waves; Homotopy perturbation method; Korteweg–de Vries nonlinear system; Laplace transform; Atangana–Baleanu operator
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-022-03709-5

In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of fractional order which uses Mittag-Leffler function as a nonsingular and nonlocal kernel. We investigate the nonlinear behavior of multi-component plasma. For this effective approach, named homotopy perturbation, transformation approach is suggested. This scheme of nonlinear model generally occurs as a characterization of waves in traffic flow, multi-component plasmas, electrodynamics, electromagnetism, shallow water waves, elastic media, etc. The main objective of this study is to provide a new class of methods, which requires not using small variables for finding estimated solution of fractional coupled frameworks and unrealistic factors and eliminate linearization. Analytical simulation represents that the suggested method is effective, accurate, and straightforward to use to a wide range of physical frameworks. This analysis indicates that analytical simulation obtained by the homotopy perturbation transform method is very efficient and precise for evaluation of the nonlinear behavior of the scheme. This result also suggests that the homotopy perturbation transform method is much simpler and easier, more convenient and effective than other available mathematical techniques.