Fractional study of a novel hyper-chaotic model involving single non-linearity
Hyperchaos; Mathematical modeling; Numerical method; Numerical simulation
The applications of hyperchaotic systems (HCSs) can be widely seen in diverse fields associated with engineering due to their complicated dynamics, randomness, and high delicacy and sensibility. In the present work, we aim to investigate a new hyper-chaotic system involving a single non-linearity under the fractional CaputoFabrizio (CF) derivative for the first time. In fact, there is no previous study using fractional derivatives in this system. A new mathematical system using a fractional-order operator will be designed with the novel operator. The CaputoFabrizio non-integer operator is aimed to be employed to capture complex nature. In order to solve the extracted dynamical system, a quadratic numerical scheme is applied. This study contains stability and convergence sections for the considered method. Moreover, numerical results of the problem under various values of fractional orders and different values of initial conditions (ICs) are provided to show the performance of the suggested scheme. Figures of solutions for each dependent variable can be observed. 2022 The Author(s)
Partohaghighi M.; Veeresha P.; Akg A.; Inc M.; Riaz M.B.
https://doi.org/10.1016/j.rinp.2022.105965 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85138053598&doi=10.1016%2fj.rinp.2022.105965&partnerID=40&md5=7aa1cafb32c9dae3a3c1cb146f3788f3
Partohaghighi M., Department of Mathematics, Clarkson University, United States; Veeresha P., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Akg A., Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, 56100, Turkey, Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, Nicosia/Mersin 10, PC: 99138, Turkey; Inc M., Department of Mathematics, Science Faculty, Firat University, Elazig, Turkey, Department of Medical Research, China Medical University, Taichung, Taiwan; Riaz M.B., Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, Lodz, 90-924, Poland, Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan