A computational approach for numerical simulations of the fractal–fractional autoimmune disease model

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-12, Vol.165, p.112829, Article 112829
• Main Authors: Ravi Kanth, A.S.V., Devi, Sangeeta
• Format: Article
• Language: English
• Subjects: Autoimmune disease model; Caputo; Fixed point theorem; Fractal–fractional operator; Numerical solution
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112829

The major goal of this study is to describe and analyse numerical simulations based on Adams–Bashforth approach for fractal–fractional order autoimmune disease framework, to explore the function of viruses in the progression of autoimmune disease. Target cells, damaged cells, viruses, and effector immune cells are all studied using the Caputo fractal–fractional operator. Fixed point theorems are used to demonstrate the existence and uniqueness of the framework. The numerical technique is described utilizing Lagrange piecewise interpolation to achieve the numerical solution for different choices of the parameters. From a biological standpoint, the influence of different factors on the system and the numerical simulation results are explored. We compare the outcomes of distinct choices of the fractal and fractional order parameters to integer order results. The proposed model captures the relevant autoimmune disease behaviour with recurrent flare-ups in the typical instance, whereas mild symptoms are emphasized in various fractional and fractal–fractional scenarios.