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Open Access Article
1 - Computational Method for Fractional-Order Stochastic Delay Differential Equations
Behrouz Parsa Moghaddam Zeynab Salamat Mostaghim Elham Alsaddat Hashemi ZadehDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order s MoreDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense. The computational method is based on bilinear spline interpolation and finite difference approximation. The convergence order of the proposed method investigated in the mean square norm and the accuracy of proposed scheme is analyzed in the perspective of the mean absolute error and experimental convergence order. The proposed method is considered in determining statistical indicators of Gompertzian and Nicholson models. The fractional stochastic delay Gompertzian equation is modeled for describing the growth process of a cancer and the fractional stochastic delay Nicholson equation is formulated for explaining a population dynamics of the well-known Nicholson blowflies in ecology. Manuscript profile -
Open Access Article
2 - Zernike radial polynomials method for solving nonlinear singular boundary value problems arising in physiology
M.A. Ebadi E.S. Hashemizadeh A.H. Refahi SheikhaniThe aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat sourc MoreThe aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat source in human head and cancer tumor growth and etc. In this paper this equations are solved by a new numerical method by using Zernike radial polynomials. In the proposed method for the first time the operational matrix of derivative for Zernike radial polynomials is derived and by using this operational matrices of derivative of Zernike radial functions the differential equation convert to a system of algebraic equations that can be solved easily. The implementation of this proposed method is simple and attractive. Finally some applied models are presented to compare the results by other method results, and they show the accuracy and efficiency of the presented method. Manuscript profile
List of Articles الهام السادات هاشمی زاده
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