Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control

Abstract

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Fractal-fractional mathematical modeling and forecasting of new cases and deaths of COVID-19 epidemic outbreaks in India

“…Moreover, these continuous improvements have expanded the use of simulations techniques and modeling based mathematics to both the generation and testing of fundamental assumptions and introduce experimental devices for controlling the spread and transmission of the disease. Modeling, simulation and analysis of these diseases have effectively clarified beforehand astounding perceptions and had a focal impact in numerous countries [4] , [5] , [6] , [7] , [8] , [9] , [10] . Both mathematical modeling and simulation play a critical role in making rapid evaluation.…”

Caputo-Fabrizio Fractional Derivative to Solve the Fractional Model of Energy Supply-Demand System

“…Yuzbasi et al [1,2] applied the exponential Galerkin method and Bessel collocation method for solving model of HIV infection of CD4+T cells. Also, Noeiaghdam and Khoshrouye Ghiasi [3,4] discussed the homotopy analysis transform method to approximate both CD4+T and CD8+T-cells and Ahmad Naik et al [5][6][7] studied the fractional model of HIV infection. Mathematical models of computer viruses were illustrated by Ozturk et al [8] using Chebyshev polynomials and its fractional form was studied by Singh et al [9] applying fractional derivative.…”

On the modeling of the interaction between tumor growth and the immune system using some new fractional and fractional-fractal operators

“…Thanks to the researchers’ efforts, many differentiated and integral operators based on different approaches were proposed and then successfully implemented in the past few years [ 1 , 4 , 5 , 10 , 13 , 23 , 25 , 30 ]. From the perspective of numerical aspects, a wide range of new mathematical methods was successfully applied in various branches of science [ 6 , 13 , 16 – 19 , 27 , 29 , 35 , 37 , 39 ]. For example, in [ 9 ] the authors have developed an efficient numerical treatment for ordinary fractional and fractal-fractional differential differential equations, which is based on Newton polynomials.…”