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- MakaleAçık Erişim2025Scopus SJRQ3Mathematical analysis of fractional order Covid 19 epidemic model
Açikgöz, Pınar; Merdan, Mehmet
This article aims to examine the dynamics of the fractional epidemic model of covid 19. The model in question incorporates the notion of a compatible derivative. Given their consistent and worldwide characteristics, fractional derivatives are presently employed to address nu-merous practical issues. In addition, we employ two numerical techniques, namely the con-formal differential transform and the variational iteration approach, to provide an approxi-mate solution for the given model. The research closes by providing an in-depth analysis and visually representing the numerical findings. Furthermore, it has been demonstrated that the solution obtained is convergent.
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İncele - MakaleAçık Erişim2025Scopus SJRQ3Investigation of fractional order covid-19 model with q-homotopy analysis transform method
Merdan, Mehmet; Açikgöz, Pınar
The primary objective of this paper is to derive approximate analytic solutions for the time fractional-order Covid-19 model by employing the q-homotopy analysis transform method (q-HATM) and the Laplace transform homotopy perturbation method (LT-HPM). The covid 19 model is a system of five-dimensional nonlinear ordinary differential equations. Moreover, this method applies even to more complex partial differential equations originating from mathematical biology, demonstrating computational efficiency and wide application. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied to analyze the approximate solutions of the system. Graphical results are presented and discussed quantitatively to illustrate the approximate solution. Copyright 2021, Yıldız Technical University.
- MakaleAçık Erişim2025Scopus SJRQ2Investigation of Nonstandard Finite Difference for Fractional Order Covid-19 Model
Merdan, Mehmet; Acikgoz, Pınar
This article examines a mathematical model of the Covid-19 type. We demonstrate how the population is impacted by immigration, protection, the mortality, exposure, curing, and interactions between sick and healthy individuals. There are five classifications in our model: exposed, susceptible, infected, quarantined, and recovered. The model is subjected to numerical and fractional analysis in this instance. The numerical analysis is performed using the fractional order non-standard finite difference (NSFD) scheme. The Grunwald-Letnikov numerical approximation technique is used for fractional analysis. The findings are evaluated by simulations using the Matlab tool.
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