Traveling Wave Solutions of Fractional Differential Equations Arising in Warm Plasma

Authors

Krishna Ghode, B. K. Birla College of Arts, Science and Commerce, Kalyan, Thane-421301, (M.S.), India.Follow
Kalyanrao Takale, RNC Arts, JDB Commerce and NSC Science College, Nashik-422101, (M.S.), India.Follow
Shrikisan Gaikwad, New Arts, Commerce and Science College, Ahmednagar-424001, (M.S.), India.Follow

Abstract

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

Keywords

Caputo fractional derivative, Fractional Adomian decomposition method, Fractional Kawahara equation, Fractional Korteweg–De Vries equation, Riemann–Liouville fractional integral

Article Type

Special Issue Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Ghode, Krishna; Takale, Kalyanrao; and Gaikwad, Shrikisan (2023) "Traveling Wave Solutions of Fractional Differential Equations Arising in Warm Plasma," Baghdad Science Journal: Vol. 20: Iss. 1, Article 27.
DOI: https://doi.org/10.21123/bsj.2023.8394