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- MakaleAçık Erişim2025Mathematical 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.
- MakaleAçık Erişim2024The novel numerical solutions for time-fractional Fornberg-Whitham equation by using fractional natural transform decomposition method
Alkan, Aslı; Anaç, Halil
The time-fractional partial differential equations were solved by the fractional natural transform decomposition method. Fractional derivatives are Caputo sense. The Fornberg-Whitham equation is a generalization of the Korteweg-de Vries (KdV) equation, which describes the propagation of long waves in shallow water. It includes higher-order dispersion terms, making it applicable to a wider range of dispersive media the fractional natural transform decomposition method (FNTDM) was also used to examine applications, and the solutions obtained by this method have been compared to those obtained by the variational iteration method, fractional variational iteration method, and homotopy perturbation method. In addition, the MAPLE package drew graphs of the solutions of nonlinear time-fractional partial differential equations, taking into account physics. The method described in this study exhibited a notable degree of computational precision and straightforwardness when used to the analysis and resolution of intricate phenomena pertaining to fractional nonlinear partial differential equations within the domains of science and technology.
- MakaleYalnız künye2013A multistage variational iteration method for solution of delay differential equations
Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat
In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.
- MakaleYalnız künye2012A multistage variational iteration method for approximateanalytic solution of avian-human influenza epidemic model
Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat
In this paper, the approximate solution of avian-human influenza epidemic model is obtained by a reliable algorithm based on an adaptation of the standard variational iteration method (VIM), which is called the multi-stage variational iteration method (MVIM). A comparison between MVIM and the Runge-Kutta method (RK-method) reveals that the proposed technique is a promising tool to solve the considered problem.
- MakaleYalnız künye2011An approximate solution of a model for HIV infection of CD4+ T cells
Merdan, M.; Gokdogan, A.; Erturk, V.S.
In this paper, the approximate solution of the differential system modeling HIV infection of CD4+ T cells is obtained by a reliable algorithm based on an adaptation of the standard variational iteration method (VIM), which is called the multi-stage variational iteration method(MSVIM). A comparison between MSVIM and the fourthorder Runge-Kutta method (RK4-method) reveal that the proposed technique is a promising tool to solve the considered problem.