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A fast numerical algorithm based on the Taylor wavelets for solving the fractional integro‐differential equations with weakly singular kernels
Author(s) -
Keshavarz Elham,
Ordokhani Yadollah
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5663
Subject(s) - mathematics , convergence (economics) , wavelet , taylor series , algebraic equation , differential equation , mathematical analysis , numerical analysis , algorithm , nonlinear system , computer science , physics , quantum mechanics , artificial intelligence , economics , economic growth
In this paper, a fast numerical algorithm based on the Taylor wavelets is proposed for finding the numerical solutions of the fractional integro‐differential equations with weakly singular kernels. The properties of Taylor wavelets are given, and the operational matrix of fractional integration is constructed. These wavelets are utilized to reduce the solution of the given fractional integro‐differential equation to the solution of a linear system of algebraic equations. Also, convergence of the proposed method is studied. Illustrative examples are included to demonstrate the validity and applicability of the technique.