Certain new models of the multi-space fractal-fractional Kuramoto-Sivashinsky and Korteweg-de Vries equations
Date
2022
Authors
Srivastava, H.M.
Saad, Khaled Mohammed
Hamanah, Walid M.
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
The main objective of this paper is to introduce and study the numerical solutions of
the multi-space fractal-fractional Kuramoto-Sivashinsky equation (MSFFKS) and the multi-space
fractal-fractional Korteweg-de Vries equation (MSFFKDV). These models are obtained by replacing
the classical derivative by the fractal-fractional derivative based upon the generalized Mittag-Leffler
kernel. In our investigation, we use the spectral collocation method (SCM) involving the shifted
Legendre polynomials (SLPs) in order to reduce the new models to a system of algebraic equations.
We then use one of the known numerical methods, the Newton-Raphson method (NRM), for solving
the resulting system of the nonlinear algebraic equations. The efficiency and accuracy of the numerical
results are validated by calculating the absolute error as well as the residual error. We also present
several illustrative examples and graphical representations for the various results which we have
derived in this paper.
Description
Keywords
generalized Mittag-Leffler function, mutli-space fractal-fractional Kuramoto-Sivashinsky equation, multi-space fractal-fractional, Korteweg-de Vries equation, spectral collocation method involving the shifted legendre polynomials, Newton-Raphson method
Citation
Srivastava, H., Saad, K., & Hamanah, W. (2022). “Certain new models of the multispace fractal-fractional Kuramoto-Sivashinsky and Korteweg-de Vries equations.” Mathematics, 10(7), 1089. https://doi.org/10.3390/math10071089