New Type Modelling of the Circumscribed Self-Excited Spherical Attractor

Mohammad Partohaghighi, Ali Akgül and Rubayyi T. Alqahtani
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Mohammad Partohaghighi: Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA
Ali Akgül: Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey
Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Mathematics, 2022, vol. 10, issue 5, 1-14

Abstract: The fractal–fractional derivative with the Mittag–Leffler kernel is employed to design the fractional-order model of the new circumscribed self-excited spherical attractor, which is not investigated yet by fractional operators. Moreover, the theorems of Schauder’s fixed point and Banach fixed existence theory are used to guarantee that there are solutions to the model. Approximate solutions to the problem are presented by an effective method. To prove the efficiency of the given technique, different values of fractal and fractional orders as well as initial conditions are selected. Figures of the approximate solutions are provided for each case in different dimensions.

Keywords: Mittag–Leffler kernel; numerical method; circumscribed self-excited spherical attractor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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