Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model DOI
Z. Avazzadeh, Hossein Hassani, M. J. Ebadi

et al.

Physica Scripta, Journal Year: 2024, Volume and Issue: 99(8), P. 085015 - 085015

Published: July 11, 2024

Abstract 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 system of nonlinear equations. significance lies potential therapeutic applications cells (HSCs), particularly context HIV infection treatment, innovative use GBPs Lagrange multipliers solving (FHSCM). aim is introduce an optimization algorithm approximating solution FHSCM using provide comprehensive exploration techniques employed this context. research methodology involves formulating derivatives GBPs, conducting convergence analysis proposed method, demonstrating accuracy method through numerical simulations. major conclusion successful introduction FHSCM, featuring control parameters novel technique. also highlights providing accurate solutions thus contributing field modeling biological medical research.

Language: Английский

Modeling and analysis of Hepatitis B dynamics with vaccination and treatment with novel fractional derivative DOI Creative Commons
Anum Zehra, Saba Jamil, Muhammad Farman

et al.

PLoS ONE, Journal Year: 2024, Volume and Issue: 19(7), P. e0307388 - e0307388

Published: July 18, 2024

These days, fractional calculus is essential for studying the dynamic transmission of illnesses, developing control systems, and solving several other real-world issues. In this study, we develop a Hepatitis B (HBV) model to observe dynamics vaccination treatment effects disease by using novel operator. Modified Atangana-Baleanu-Caputo (MABC) new definition used derivative that based on modification Atangana Baleanu derivatives. By employing MABC derivative, which incorporates concepts non-locality memory our captures complex HBV more accurately than traditional models. An objective study analyze effect immunization techniques course hepatitis virus, with particular focus changing order differentiation. Thereby, paper deals stability analysis, positiveness, existence uniqueness solution simulations. Analysis reproductive number R 0 impact different parameters also treated. The proposed model’s findings are examined through use Banach’s fixed point Leray-Schauder nonlinear alternative theorems. equilibria models determined be globally stable Lyapunov functions. simulations certain achieved applying Lagrange interpolation numerical computations results compared ABC operator results. validated simulations, assess how well intervention work lower infection prevent its spread throughout community. research assist in public health policies intended incidence worldwide offer insightful information about strategies disease.

Language: Английский

Citations

11
An optimization method for solving a general class of the inverse system of nonlinear fractional order PDEs DOI
Z. Avazzadeh, Hossein Hassani, M. J. Ebadi

et al.

International Journal of Computer Mathematics, Journal Year: 2024, Volume and Issue: 101(2), P. 138 - 153

Published: Feb. 1, 2024

In this paper, we introduce a general class of the inverse system nonlinear fractional order partial differential equations (GCISNF-PDEs) with initial-boundary and two overdetermination conditions. An optimization method is considered based on generalized shifted Legendre polynomials (GSLPs) for solving GCISNV-FPDEs. The concept derivatives (F-Ds) utilized in Caputo type. Operational matrices (OMs) classical F-Ds GSLPs are extracted. Making use GSLPs, OMs, Lagrange multipliers method, reduce given GCISNF-PDEs into an algebraic equations. proposed approach achieves satisfactory results simply small number novel GSLPs. work, mathematical examples illustrated to analyse introduced convergence test its validity as well applicability.

Language: Английский

Citations

6
A Stable Finite Volume Method for Numerical Solution of Time-Tempered Fractional Sine–Gordon Equations DOI
M. Abbasi, M. Ahmadinia, Pejman Hadi

et al.

Deleted Journal, Journal Year: 2024, Volume and Issue: 48(3), P. 637 - 647

Published: March 23, 2024

This paper proposes a numerical method based on the finite volume for solving time-tempered fractional sine–Gordon equation. To overcome nonlinearity of equation, fixed-point is employed to linearize Additionally, novel approach utilizing Discrete Gronwall Lemma has been introduced prove stability method. The provided examples demonstrate effectiveness and validate presented theory.

Language: Английский

Citations

2
Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model DOI
Z. Avazzadeh, Hossein Hassani, M. J. Ebadi

et al.

Physica Scripta, Journal Year: 2024, Volume and Issue: 99(8), P. 085015 - 085015

Published: July 11, 2024

Abstract 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 system of nonlinear equations. significance lies potential therapeutic applications cells (HSCs), particularly context HIV infection treatment, innovative use GBPs Lagrange multipliers solving (FHSCM). aim is introduce an optimization algorithm approximating solution FHSCM using provide comprehensive exploration techniques employed this context. research methodology involves formulating derivatives GBPs, conducting convergence analysis proposed method, demonstrating accuracy method through numerical simulations. major conclusion successful introduction FHSCM, featuring control parameters novel technique. also highlights providing accurate solutions thus contributing field modeling biological medical research.

Language: Английский

Citations

0