Presentation of two models for the numerical analysis of fractional integro-differential equations and their comparison
Subject Areas : Statistics
M.
Behroozifar
1
(Professor, Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Mazandaran, Iran)
Keywords: ماتریس عملیاتی مشتق مرتبه کسری کاپوتو, تکنیک نقطه گذاری, ماتریس عملیاتی انتگرال مرتبه کسری ریمان-لیوویل, ماتریس عملیاتی, معادله دیفرانسیل-انتگرال کسری,
Abstract :
In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractionalderivative method and the Riemann-Liouville fractional integral method. In the both method, a set of linear or nonlinear algebraic equations are achieved using collocation technique. Tow presented methods are implemented on some test problems. Numerical results explain the high performance of tow methods. Note that all calculations have been done by Mathematica software. Numerical results show that it should be used the first method when the exact solution of differential equation is a polynomial and the second method should be used when the exact solution of differential equation is a transcendental function.
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