Dynamic 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 More
Dynamic 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.
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In this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integr More
In this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integro-differential equations reduced to the solution of algebraic equations. Then, by solving the system of algebraic equations, the solution of the differential-integral equation is presented as a function in the terms of Chelyshkov polynomials. Accuracy and error analysis have been investigated and since the accuracy of the obtained results for fractional integro-differential equations depends on the number of selected Chelyshkov polynomials therefore, with the increase in the number of Chelyshkov polynomials, we can achieve desirable accuracy step by step. All calculations are done by MATLAB software. Also, the numerical results of based on Chelyshkov polynomials method are compared with the results of some of the available methods for the validity, accuracy and efficiency of the technique.
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In this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature r More
In this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature rule. In this ‎method, we use Gaussian radial basis function and don't distinguish between time and place ‎variables and the collocation points have both the coordinates of time and space. We use the ‎Sinc quadrature rule with single exponential transformation to approximate the integral part of ‎fractional derivatives. The chosen fractional derivatives is Riemann – Liouville.‎This method is implemented on two examples with different values of the fractional ‎derivative order. Obtained results illustrate the effectiveness of our method and sh ow that ‎one can obtain accurate results with a small number of the collocation points for the radial ‎basis function. It should be noted that all calculations in this paper have been done using ‎Mathematica software.‎
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در این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدل‌های آیکدا و هاتچینسو More
در این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدل‌های آیکدا و هاتچینسون غیرموضعی تأخیری با استناد مفاهیم خطا و همگرایی روشهای عددی به ازای مقادیر مختلف پارامترهای مرتبه کسری نمایان شده است.
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