Stability Results for Two-Dimensional Systems of Fractional-Order Difference Equations

Fractional-variable-order digital controller design tuned with the chaotic yellow saddle goatfish algorithm for the AVR system

In this paper, an optimisation method utilising the yellow saddle goatfish algorithm (YSGA) with a new fitness function is proposed to design two types of fractional-variable-order PID (FVOPID) digital controllers for the automatic voltage regulator (AVR) system. Simulations and comparisons of the results are presented, showing that variable-order control can perform better than the existing solutions for the AVR system. Additionally, we include a stability analysis of a closed-loop system by utilisation of the Nyquist stability criterion.

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo-Fabrizio Derivative

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of CD4+ T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4⁺ T-cells depending on the viral load via the Caputo–Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new CD4+ T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of CD4+ T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations.