New Type Modelling of the Circumscribed Self-Excited Spherical Attractor

Mohammad Partohaghighi,Ali Akgül,Rubayyi T Alqahtani

doi:10.3390/math10050732

Mohammad Partohaghighi, Ali Akgül + Show 1 more

Open Access

https://doi.org/10.3390/math10050732

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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.

Highlights

Classification of specific systems which are able to display chaotic behavior is one of the most interesting subjects in nonlinear problems [1–5]
Due to the importance of chaotic performance in dynamical systems, various studies have been conducted on the special properties of chaotic and nonlinear systems
Some works on megastable dynamical systems have been done which can be seen in [10–12]

Summary

Introduction

Classification of specific systems which are able to display chaotic behavior is one of the most interesting subjects in nonlinear problems [1–5]. Modeling and analysis of fractional order Ebola virus model with Mittag–Leffler kernel was reported in [25]. Fractional modelling and simulations of the SEIR and Blood Coagulation systems can be read in [26]. Modeling and analysis of fractional order Zika model can be read in [27]. A numerical and analytical study of SE (Is)(Ih) AR epidemic fractional-order COVID-19 model can be seen in [30]. In order to make fractional model of the system (1), some definitions are required. The fractal-fractional derivative of u of order α is defined as:. Analysis of fractal–fractional differential equations can be seen in [47]. Another application of FFM operator to reaction-diffusion model was reported in [48].

Existence and Uniqueness Results

Numerical Experiments

Conclusions