Laguerre polynomial solutions of linear fractional integro-differential equations
| Autor: | Dilek Varol, Ayşegül Daşcıoğlu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Differential equation Collocation Method Fractional Fredholm-Volterra integro-differential equations Conformable fractional derivative 01 natural sciences Matrix (mathematics) Numerical-Solution Applied mathematics Laguerre polynomials 0101 mathematics Approximation Mathematics Numerical Analysis Collocation Applied Mathematics 010102 general mathematics Conformable matrix Convergence Analysis Computer Science Applications Fractional calculus 010101 applied mathematics Algebraic equation Transformation (function) Homotopy Perturbation Method Signal Processing Order Analysis Information Systems |
| Zdroj: | Mathematical Sciences. 15:47-54 |
| ISSN: | 2251-7456 2008-1359 |
| DOI: | 10.1007/s40096-020-00369-y |
| Popis: | In this paper, the numerical solutions of the linear fractional Fredholm-Volterra integro-differential equations have been investigated. For this purpose, Laguerre polynomials have been used to develop an approximation method. Precisely, using the suitable collocation points, a system of linear algebraic equations arises which is resulted by the transformation of the integro-differential equation. The fractional derivative is considered in the conformable sense, and the conformable fractional derivative of the Laguerre polynomials is obtained in terms of Laguerre polynomials. Additionally, for the first time in the literature, the exact matrix formula of the conformable derivatives of the Laguerre polynomials is established. Furthermore, the results of the proposed method have been given applying the method to some various examples. |
| Databáze: | OpenAIRE |
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