Abstract:
This paper introduces a new numerical technique based on the implicit spectral collocation method and the fractional Chelyshkov basis functions for solving the fractional Fredholm integro-differential equations. The framework of the proposed method is to reduce the problem into a nonlinear system of equations utilizing the spectral collocation method along with the fractional operational integration matrix. The obtained algebraic system is solved using Newton's iterative method. Convergence analysis of the method is studied. The numerical examples show the efficiency of the method on the problems with non-smooth solutions.
Citation:
Y. Talaei, S. Noeiaghdam, H. Hosseinzadeh, “Numerical solution of fractional order Fredholm integro-differential equations by spectral method with fractional basis functions”, Bulletin of Irkutsk State University. Series Mathematics, 45 (2023), 89–103
\Bibitem{TalNoeHos23}
\by Y.~Talaei, S.~Noeiaghdam, H.~Hosseinzadeh
\paper Numerical solution of fractional order Fredholm integro-differential equations by spectral method with fractional basis functions
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2023
\vol 45
\pages 89--103
\mathnet{http://mi.mathnet.ru/iigum536}
\crossref{https://doi.org/10.26516/1997-7670.2023.45.89}
Linking options:
https://www.mathnet.ru/eng/iigum536
https://www.mathnet.ru/eng/iigum/v45/p89
This publication is cited in the following 4 articles:
Nouria Arar, Bouchra Deghdough, Souad Dekkiche, Zineb Torch, A. M. Nagy, “Numerical Solution of the Burgers' Equation Using Chelyshkov Polynomials”, Int. J. Appl. Comput. Math, 10:1 (2024)
A. H. Tedjani, A. Z. Amin, Abdel-Haleem Abdel-Aty, M. A. Abdelkawy, Mona Mahmoud, “Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis”, MATH, 9:4 (2024), 7973
Muhammad Sarwar, Aiman Mukheimer, Syed Khayyam Shah, Arshad Khan, “Existence of solutions of fractal fractional partial differential equations through different contractions”, MATH, 9:5 (2024), 12399
V. M. Abdullaev, “K resheniyu nagruzhennykh differentsialnykh uravnenii s nelokalnymi usloviyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 45–62