A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

Alshehri, Hashim M.; Khan, Aziz

doi:10.1155/2021/2524027

Cited by 9 publications

(3 citation statements)

References 23 publications

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“…The ensuing collection of articles encompasses a diverse array of mathematical models, addressing various subjects. These models explore the dynamics of disease spread and control, with specific applications to notable infections like COVID-19, 24,25 hepatitis C, 26 and also extend to other domains such as chaotic circuits, 27 environmental persistence of infections, 28 Langevin systems, 29 computer viruses, 30 thermostat control models, 31,32 stochastic models, 33 resource-consumer dynamics, 17 Navier systems, 34 quantum systems, 35 among others. [36][37][38][39] Fractional calculus represents a mathematical domain that extends the principles of differentiation and integration to non-integer orders.…”

Section: Introductionmentioning

confidence: 99%

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

Khan,

ur Rahman,

Arfan

et al. 2024

Int J Numerical Modelling

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The current manuscript investigates a six compartmental mathematical model for malicious Codes in Wireless Sensor Network is consider for investigation under the fractional operator of Caputo along with their numerical scheme. The six agent nodes of the network sensors are transferable like in infection with in their community of different nodes. With the help of fixed point theory the presentation of existence and uniqueness of solution of the said model are also given. The scheme of numerical solution under fractional format is developed with the choice of fractional orders which increasing the degree of freedom for such type of network analysis. The numerical simulation of all the six agents are given on different fractional orders along with sensitivity of the fractional orders and some used parameters. The new analysis artificial neural network (ANN) method has been utilized for the considered model and compared with Adams–Bashforth (AB) method. We divided the data set into three categories training, testing and validation with ANN method and the analysis is presented in this work.

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Section: Introductionmentioning

confidence: 99%

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

Khan,

ur Rahman,

Arfan

et al. 2024

Int J Numerical Modelling

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“…These operators are based on the singular and nonsingular kernels as well as local and nonlocal kernels. Readers can peruse some related literature given in [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay

Telli

Souid

Alzabut

et al. 2023

Axioms

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This study establishes the existence and stability of solutions for a general class of Riemann–Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay. Our findings are confirmed by the fixed-point theorems (FPTs) from the available literature. We transform the RL FDE of variable order to alternate RL fractional integral structure, then with the use of classical FPTs, the existence results are studied and the Hyers–Ulam stability is established by the help of standard notions. The approach is more broad-based and the same methodology can be used for a number of additional issues.

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“…You can examine these functions and integrals using the references. Fractional differential operators are becoming robust, and systematic mathematical tools for studying various scientific and biological events nowadays, for example, childhood disease [14,16], HIV, coronary heart disease [15], hepatitis C [17], Chikungunya virus [18], and Crimean-Congo hemorrhagic fever (CCHF) [19], can be seen in the references. Fractional-order differential equations, in contrast to integer-order differential equations, can show nonlocal interactions with memory cores in time and space [6,7].…”

Section: Introductionmentioning

confidence: 99%

$A B C$ Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination

Yang

Afzal

Appiah

2022

Advances in Mathematical Physics

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Chickenpox or varicella is an infectious disease caused by the varicella-zoster virus V Z V . This virus is the cause of chickenpox (usually a primary infection in the nonimmune host) and herpes zoster. In this paper, a compartmental model for the dynamics of V Z transmission with the effect of vaccination is solved using the A B C fractional derivative. The possibility of using the fractal dimension as a biomarker to identify different diseases is being investigated. The problem is investigated in two different levels of research using two scale dimensions. To ascertain the existence and uniqueness of the solution, we qualitatively evaluate the model. We have used the Euler method to compute the numerical solution for the system. At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.

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A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

Cited by 9 publications

References 23 publications

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay

$A B C$ Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination

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A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

Cited by 9 publications

References 23 publications

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay

A B C Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination

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Product

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$A B C$ Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination