Numerical solution of fractional integro-differential equations by collocation method

Applied Mathematics and Computation (Impact Factor: 1.55). 05/2006; 176(1):1-6. DOI: 10.1016/j.amc.2005.09.059
Source: DBLP


This paper deals with the numerical solution of fractional integro-differential equations of the typeDqy(t)=p(t)y(t)+f(t)+∫0tK(t,s)y(s)ds,t∈I=[0,1]by polynomial spline functions. We derive a system of equations that characterizing the numerical solution. Some numerical examples are also provided to illustrated our results.

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    • "In [28], fractional differential transform method was developed to solve FIDE's with nonlocal boundary conditions. In [33], Rawashdeh studied the numerical solution of FIDE's by polynomial spline functions. In [36], authors solved fractional nonlinear Volterra integro differential equations using the second kind Chebyshev wavelets. "
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    ABSTRACT: In this paper, we develop a fully Discrete Galerkin(DG) method for solving initial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(GJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method.
    Acta Mathematica Scientia 10/2015; · 0.74 Impact Factor
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    • "For instance we can mention the following works. Lepik [33] applied the Haar wavelet method to solve the fractional integral equations, Momani et al. [38] applied the Adomian decomposition method to approximate solutions for fourth-order fractional integrodifferential equations, Rawashdeh [43] applied collocation method to study integro-differential equations of fractional order. Moreover, properties of these equations have been studied by several authors [1] [3] [51]. "
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    ABSTRACT: The purpose of the present paper is to propose an efficient numerical method for solving the differential equations of Bratu-type with fractional order in reproducing kernel Hilbert space. The exact solution is calculated in the form of a convergent series with easily computable components. Finally, some examples are given to illustrate the efficiency and applicability of the method. Copyright © 2015 John Wiley & Sons, Ltd.
    Mathematical Methods in the Applied Sciences 07/2015; DOI:10.1002/mma.3588 · 0.92 Impact Factor
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    • "There are four kinds of Chebyshev polynomials as in [14]. The majority of books dealing with Chebyshev polynomials, contain mainly results of Chebyshev polynomials of all kinds T n ðxÞ; U n ðxÞ; V n ðxÞ and W n ðxÞ and their numerous uses in different applications, and research papers dealing with some types of these polynomials (see for instance, [1] [2] [16] [17] also see, [22] [23] [24] [25] [26] [27] [28] and other publications as [4] [7] [8] [12] [20]). However, there are only a limited researches of literature on shifted Chebyshev polynomials of the second kind U Ã n ðxÞ , either from theoretical or practical points of view it uses in various applications. "
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    ABSTRACT: In this paper, an efficient numerical method for solving space fractional order diffusion equation is presented. The numerical approach is based on shifted Chebyshev polynomials of the second kind where the fractional derivatives are expressed in terms of Caputo type. Space fractional order diffusion equation is reduced to a system of ordinary differential equations using the properties of shifted Chebyshev polynomials of the second kind together with Chebyshev collocation method. The finite difference method is used to solve this system of equations. Several numerical examples are provided to confirm the reliability and effectiveness of the proposed method.
    Chaos Solitons & Fractals 04/2015; 73. DOI:10.1016/j.chaos.2015.01.010 · 1.45 Impact Factor
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