Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator

Yadav, Pooja; Jahan, Shah; Shah, Kamal; Peter, Olumuyiwa James; Abdeljawad, Thabet

doi:10.1016/j.aej.2023.09.006

Cited by 28 publications

(2 citation statements)

References 31 publications

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“…Their research highlighted the importance of the dynamics of epidemic infection rate and reproduction capacity. The significance and broad applicability of fractional models [ 11 ] and nonlinear dynamical systems through the differential transform [ 12 ]. In recent studies researchers have explored various aspects of fractional analysis in different contexts.…”

Section: Introductionmentioning

confidence: 99%

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Nisar,

Farman,

Jamil

et al. 2024

PLoS ONE

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In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel’a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton’s polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

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Section: Introductionmentioning

confidence: 99%

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Nisar,

Farman,

Jamil

et al. 2024

PLoS ONE

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show abstract

“…The application of fractional calculus, encompassing both integration and fractional differentiation, offers a more comprehensive insight into real-world challenges than the conventional integer-order calculus. Additionally, it excels at representing and modeling real-world phenomena, primarily owing to its capacity to account for the memory and inherent properties, as substantiated in [28] – [30] . The concept of fractional derivatives lacks a universally accepted definition; instead, it encompasses several distinct formulations, including the Riemann–Liouville, Liouville–Caputo, Grunwald–Letnikov, and other variations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative

Yadav,

Jahan,

Nisar

2024

AIMSPH

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<abstract> <p>Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid-<italic>β</italic> ($\mathbb{ A_\beta }$), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders.</p> </abstract>

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Modelling the impact of education and memory on the management of diabetes mellitus using Atangana-Baleanu-Caputo fractional order model

Olayiwola,

Alaje,

Yunus

2024

Nonlinear Dyn

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Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator

Cited by 28 publications

References 31 publications

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative

Modelling the impact of education and memory on the management of diabetes mellitus using Atangana-Baleanu-Caputo fractional order model

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