Atangana-Baleanu Operators Research Articles

Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics

In this paper, we propose a high-gain observer to synchronize chimera states in coupled neurons with fractional dynamics. The observer allows the synchronization with a master–slave topology. The master describes a dynamical system in state-space representation, whereas the slave is described by a high-gain state observer. The fractional differential equations are described by the Riemann–Liouville fractional derivative, also for non-local conformable derivatives and Atangana–Baleanu operators both in Caputo sense. We present numerical simulations involving the synchronization of Hindmarsh–Rose and Hodgking–Huxley models. The numerical simulations showed that the chimera states can be synchronized using fractional derivatives. We believe that the application of fractional operators to synchronization of Chimera states open a new direction of research in the near future.

The Failure of Certain Fractional Calculus Operators in Two Physical Models

Abstract The ability of the so-called Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) operators to create suitable models for real data is tested with real world data. Two alternative models based on the CF and AB operators are assessed and compared with known models for data sets obtained from electrochemical capacitors and the human body electrical impedance. The results show that the CF and AB descriptions perform poorly when compared with the classical fractional derivatives.

Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives.

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter , the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two.