Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws. (English) Zbl 1374.34296
Summary: The nature is very complex to model with mathematical equations. Some physical problems found in nature could follow the power law; other could follow the Mittag-Leffler law and other the exponential decay law. On the other hand one could observe in nature a physical problem that combines both, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator exponential-Mittag-Leffler kernel with two fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed.
MSC:
| 34K23 | Complex (chaotic) behavior of solutions to functional-differential equations |
| 65L04 | Numerical methods for stiff equations |
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
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