A numerical efficient splitting method for the solution of HIV time periodic reaction–diffusion model having spatial heterogeneity

Raza, Nauman; Arshed, Saima; Bakar, Abu; Shahzad, Aamir; İnç, Mustafa

doi:10.1016/j.physa.2022.128385

Cited by 6 publications

(1 citation statement)

References 31 publications

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“…They explored the positivity and boundedness of solutions and analyzed equilibrium points with reproduction numbers. Raza et al [25] examined a reaction-diffusion model concerning acquired immunodeficiency syndrome, focusing on its presence and management. Their investigation included identifying equilibrium points and threshold parameters for the model, along with introducing a novel nonstandard operator splitting technique to solve it.…”

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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Section: Introductionmentioning

confidence: 99%