Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations

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.

الحلول العددية لمعادلات أبيل التكاملية الخطية بطريقة متعددات حدود بوبكر

“…The comparison appeared that the suggested technique gives the same precise solution as this example. Also 8,9,19,20 , the precise solution he had when r =3. As a result, these five techniques are identical in terms of accuracy of the results.…”

“…In recent years, the (LAI) Eq numerical solution has been the focus of intense research by academics. Among their works are some of the following methods: Taylor-collocation approach 5 , Lagrangian matrix technique 6 , Chebyshev polynomials 7 , Touchard Polynomials 8 , Orthogonal polynomials method 9 , the product integration and Haar Wavelet techniques 10 wavelet approach 11 , Babenko and fractional integrals methods 12 , Babenko and fractional calculus techniques 13 , Mechanical quadrature method 14 . The following is how the rest of the article is structured: the proposed method, approximation function, solution accuracy, solutions Abel integral Eq, and numerical examples.…”