Open AccessANALYSIS OF TIME-FRACTIONAL KAWAHARA EQUATION UNDER MITTAG-LEFFLER POWER LAW
Author(s) -
Mati ur Rahman,
Muhammad Arfan,
Wejdan Deebani,
Poom Kumam,
Zahir Shah
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400217
Subject(s) - adomian decomposition method , mathematics , fractional calculus , laplace transform , nonlinear system , operator (biology) , integer (computer science) , polynomial , mathematical analysis , differential equation , computer science , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene , programming language
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.