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

Kanth, A. S. V. Ravi; Devi, Sangeeta

doi:10.1016/j.chaos.2022.112829

Cited by 5 publications

(3 citation statements)

References 33 publications

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“…Another interesting approach is the modeling using fractional differential equations allowing the consideration of memory effects [25][26][27][28][29][30][31]. During the last decade this approach has been successfully used for modeling the development of such diseases as HIV, COVID-19 and toxoplasmosis etc.…”

Section: Mathematical Modeling In Medicinementioning

confidence: 99%

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On a Mathematical Model of a General Autoimmune Disease

Kolev,

Netov,

Nikolova

et al. 2023

Axioms

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The proposed paper is devoted to presenting and analyzing a kinetic model describing the development of autoimmune disorders. The proposed model is a nonlinear system of differential equations that considers the biological activity of the interacting populations. The main characteristics of autoimmune diseases are taken into account. Preliminaries to the research area are provided. The modeling problem is discretized and solved approximately. The numerical results illustrate typical outcomes of autoimmune diseases.

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Section: Mathematical Modeling In Medicinementioning

confidence: 99%

“…The paper [26] is devoted to applying fractional calculus to study the development of autoimmune diseases. The authors extend the model proposed in [32] by applying the Caputo fractal-fractional operator.…”

Section: Mathematical Modeling In Medicinementioning

confidence: 99%

On a Mathematical Model of a General Autoimmune Disease

Kolev,

Netov,

Nikolova

et al. 2023

Axioms

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“…Several studies have demonstrated the effectiveness of these techniques in capturing the inherent memory effects and non-local properties of various systems [20][21][22]. Kanth and Devi [23] conducted numerical simulations based on the Adams-Bashforth approach for a fractal-fractional order autoimmune disease framework, aiming to investigate the role of viruses in autoimmune disease progression. Jain et al [24] developed a fractional model of influenza disease using Caputo, Caputo-Fabrizio, and Atangana-Baleanu derivatives, which incorporate nonlocal and non-singular properties.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model

Avazzadeh,

Hassani,

Ebadi

et al. 2024

Phys. Scr.

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The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), particularly in the context of HIV infection treatment, and the innovative use of GBPs and Lagrange multipliers in solving the fractional hematopoietic stem cells model (FHSCM). The aim of the study is to introduce an optimization algorithm for approximating the solution of the FHSCM using GBPs and Lagrange multipliers, and to provide a comprehensive exploration of the mathematical techniques employed in this context. The research methodology involves formulating operational matrices for fractional derivatives of GBPs, conducting a convergence analysis of the proposed method, and demonstrating the accuracy of the method through numerical simulations. The major conclusion is the successful introduction of GBPs in the context of the FHSCM, featuring innovative control parameters and a novel optimization technique. The study also highlights the significance of the proposed method in providing accurate solutions for the FHSCM, thus contributing to the field of mathematical modeling in biological and medical research.

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