Abstract
In this paper, a collocation method based on the orthogonal polynomials is presented to solve the fractional integral equations. Six numerical examples are given to illustrate the method. The results are compared with the other methods in the literature, and the results obtained by different kinds of polynomials are compared.
Highlights
Fractional analysis is used in many fields such as fluid flow of science and engineering, rheology, electromagnetic theory, and probability [1,2,3]
The aim of this study is to develop a collocation method, and to give a comparison for solving the fractional integral equations with orthogonal polynomials such as Jacobi, Legendre, Chebyshev, Hermite, and Laguerre polynomials
A collocation method based on the orthogonal polynomials has been presented to solve Volterra integral equations which contain fractional, Abel and singular integrals
Summary
Fractional analysis is used in many fields such as fluid flow of science and engineering, rheology, electromagnetic theory, and probability [1,2,3]. Numerical methods on other fractional integral equations are hybrid collocation [37], smoothing technique [38], piecewise constant orthogonal functions approximation [39], the Haar wavelet method [40], the Galerkin method [41], Bernstein’s approximation [42,43], the Simpson 3/8 rule method [44], mechanical quadrature [45], Legendre. The aim of this study is to develop a collocation method, and to give a comparison for solving the fractional integral equations with orthogonal polynomials such as Jacobi, Legendre, Chebyshev, Hermite, and Laguerre polynomials. More details about these orthogonal polynomials can be found in [48,49,50].
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