New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments

Sweilam, N. H.; AL–Mekhlafi, S.M.; Hassan, Syed Tajuddin Syed; Alsenaideh, Nehaya R.; Radwan, A. M.

doi:10.3390/math10234579

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…A fractional model of the within-host dynamics of SARS-CoV-2 is presented in [24] using the Caputo fractional order operator. The dynamics of COVID-19 are modeled in [25] using a new hybrid fractional order operator (a linear combination of Riemann-Lioville and Caputo). Most researchers are optimistic about the fractional order differential equation, especially in biological modeling [26].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Mohandoss,

Chandrasekar,

Meetei

et al. 2024

Axioms

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This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease.

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Section: Introductionmentioning

confidence: 99%

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Mohandoss,

Chandrasekar,

Meetei

et al. 2024

Axioms

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“…This led to a fuzzy fractional diffusion equation. As discussed by many researchers, the cancer tumor model can be represented by a fractional diffusion equation [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ]. However, in reality, the crisp quantities of the cancer tumor model are deemed uncertain.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells

Zureigat

Al‐Smadi

Al-Khateeb

et al. 2023

IJERPH

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A cancer tumor model is an important tool for studying the behavior of various cancer tumors. Recently, many fuzzy time-fractional diffusion equations have been employed to describe cancer tumor models in fuzzy conditions. In this paper, an explicit finite difference method has been developed and applied to solve a fuzzy time-fractional cancer tumor model. The impact of using the fuzzy time-fractional derivative has been examined under the double parametric form of fuzzy numbers rather than using classical time derivatives in fuzzy cancer tumor models. In addition, the stability of the proposed model has been investigated by applying the Fourier method, where the net killing rate of the cancer cells is only time-dependent, and the time-fractional derivative is Caputo’s derivative. Moreover, certain numerical experiments are discussed to examine the feasibility of the new approach and to check the related aspects. Over and above, certain needs in studying the fuzzy fractional cancer tumor model are detected to provide a better comprehensive understanding of the behavior of the tumor by utilizing several fuzzy cases on the initial conditions of the proposed model.

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Mathematical Modeling of Cancer Tumor Dynamics with Multiple Fuzzification Approaches in Fractional Environment

Qayyum,

Tahir

2023

Interdisciplinary Cancer Research

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New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments

Cited by 6 publications

References 31 publications

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells

Mathematical Modeling of Cancer Tumor Dynamics with Multiple Fuzzification Approaches in Fractional Environment

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