An efficient approach for fractional nonlinear chaotic model with Mittag-Leffler law
AB derivative; Chaotic system; Fixed point theorem; Homotopy analysis method; Laplace transform
In this work, we exemplify the behaviour of the nonlinear model of arbitrary order differential equations by adopting q-homotopy analysis transform method (q-HATM). In the present study, the illustrated scheme is a graceful amalgamation of Laplace transform with q-homotopy analysis algorithm and we considered arbitrary order derivative using Atangana-Baleanu (AB) operator. The suggested nonlinear system exhibits chaotic behaviour in nature with respect to considered initial conditions. Fixed point hypothesis heard present the existence and uniqueness for the attained solution. We exemplified suggested arbitrary order system with to illustrate and confirm the efficiency of the projected solution procedure. Further, the numerical simulation is illustrated and also the chaotic behaviour of the obtained result captured with respect to arbitrary order in terms of plots. The obtained results confirm the projected scheme is highly methodical, easy to implement and very powerful to exemplify the nature of the dynamical system of arbitrary order. 2021 The Author(s)
Veeresha P.; Prakasha D.G.; Abdel-Aty A.-H.; Singh H.; Mahmoud E.E.; Kumar S.
Journal of King Saud University - Science, Vol-33, No. 2
https://doi.org/10.1016/j.jksus.2021.101347 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85100250207&doi=10.1016%2fj.jksus.2021.101347&partnerID=40&md5=98c594b7db3a907de0f06626a5343891
Veeresha P., Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Prakasha D.G., Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere, 577007, Karnataka, India; Abdel-Aty A.-H., Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha, 61922, Saudi Arabia, Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt; Singh H., Department of Mathematics, Post-Graduate College Ghazipur, 233001, Uttar Pradesh, India; Mahmoud E.E., Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt; Kumar S., Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India