New Type Modelling of the Circumscribed Self-Excited Spherical Attractor
Open Access
- 25 February 2022
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 10 (5), 732
- https://doi.org/10.3390/math10050732
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
This publication has 49 references indexed in Scilit:
- Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex systemChaos, Solitons, and Fractals, 2017
- Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variableAEU - International Journal of Electronics and Communications, 2017
- Megastability: Coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially-periodic dampingThe European Physical Journal Special Topics, 2017
- Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuitNonlinear Dynamics, 2017
- Variable-boostable chaotic flowsOptik, 2016
- A Tutorial Review on Fractal Spacetime and Fractional CalculusInternational Journal of Theoretical Physics, 2014
- On the local fractional derivativeJournal of Mathematical Analysis and Applications, 2010
- Topological study of multiple coexisting attractors in a nonlinear systemJournal of Physics A: Mathematical and Theoretical, 2009
- Multiple delay Rössler system—Bifurcation and chaos controlChaos, Solitons, and Fractals, 2008
- Some simple chaotic flowsPhysical Review E, 1994