Browsing by Author "Sayed, Amaal"

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Numerical behavior of a fractional order dynamical model of RNA silencing
(International Journal of Scientific World, 2016) El-Sayed, AMA; Khalil, M; Arafa, AAM; Sayed, Amaal
A class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.
On a Fractional Variable-Order Model of MERS-CoV
(Natural Sciences Publishing, 2023-04) Khalil, Mohamed; Arafa, Anas; Sayed, Amaal
In this paper, a non-integer variable-order epidemiological model is presented to study the human-to-human transmission of Middle East respiratory syndrome coronavirus (MERS-CoV) pandemic in two areas. In the presented SISImodel, the human population is divided into two compartments; susceptible and infectious compartments. The impact of the memory which changes with time in the sense of Caputo’s derivative of fractional variable-order is studied through the numerical solutions of the proposed model. The numerical solutions are obtained via predictor corrector method. Moreover, the equilibrium points and stability of the model are illustrated. © 2023 NSP Natural Sciences Publishing
Two Different Functions of A Variable-Order Fractional Derivative for A Vector Host Model
(2021-01) Sayed, Amaal; Khalil, M; Arafa, A.M.A
Fractional calculus is one of the best mathematical tools to characterize the memory property of the dynamical systems. So, Variable-order fractional derivatives in Caputo sense are used in characterizing the memory property of the presented dynamic a vector host model. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. These numerical solutions show that the modeling of vector host model with variable-order fractional derivatives has more advantaged than integer-order derivatives.