ANALYSIS OF TIME-FRACTIONAL KAWAHARA EQUATION UNDER MITTAG-LEFFLER POWER LAW

Mati Ur Rahman (), Muhammad Arfan (), Wejdan Deebani (), Poom Kumam and Zahir Shah ()
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Mati Ur Rahman: Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, P. R. China
Muhammad Arfan: Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
Wejdan Deebani: Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia
Poom Kumam: KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand5Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Zahir Shah: Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-13

Abstract: In this paper, we study a newly updated nonlinear fractional Kawahara equation (KE) using Atangana–Baleanu fractional operator in the sense of Caputo (ABC). To find the approximate solution, one of the famous techniques of the Laplace Adomian decomposition method (LADM) is used along with a time-fractional derivative. For evaluation, the required quantity is decomposing into small particles along with the application of Adomian polynomial to the nonlinear term. By the addition of the first few evaluating terms, the required convergent quantity is obtained. To explain the authenticity and the manageability of the procedure, few examples are present at different fractional orders both in three and two dimensions. Further, to compare the obtained results between fractional derivative and integer derivative, some graphical presentations are given. So, the newly updated version of the KE equation is analyzed in fraction operator providing the whole density of the total dynamics at any fractional value between two different integers.

Keywords: KE; Time-Fractional Derivative; ABC Fractional Derivative Operator (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400217

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