Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions
In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/6647128 |
| _version_ | 1797378804876836864 |
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| author | S. Akhlaghi M. Tavassoli Kajani M. Allame |
| author_facet | S. Akhlaghi M. Tavassoli Kajani M. Allame |
| author_sort | S. Akhlaghi |
| collection | DOAJ |
| description | In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville fractional integral corresponding to this kind of Müntz functions. Then, using the Gauss–Legendre quadrature rule and by employing the roots of Müntz functions as the collocation points, we arrive at a system of algebraic equations. By solving this system, an approximate solution for the fractional-order integro-differential equation is obtained. We also construct an upper bound for the truncation error of Müntz orthogonal functions, and we analyze the error of the proposed collocation method. Numerical examples are included to demonstrate the validity and accuracy of the method. |
| first_indexed | 2024-03-08T20:12:54Z |
| format | Article |
| id | doaj.art-46ed682d212f44b5b1cf7c757badb5fb |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-08T20:12:54Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-46ed682d212f44b5b1cf7c757badb5fb2023-12-23T00:00:03ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/6647128Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal FunctionsS. Akhlaghi0M. Tavassoli Kajani1M. Allame2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville fractional integral corresponding to this kind of Müntz functions. Then, using the Gauss–Legendre quadrature rule and by employing the roots of Müntz functions as the collocation points, we arrive at a system of algebraic equations. By solving this system, an approximate solution for the fractional-order integro-differential equation is obtained. We also construct an upper bound for the truncation error of Müntz orthogonal functions, and we analyze the error of the proposed collocation method. Numerical examples are included to demonstrate the validity and accuracy of the method.http://dx.doi.org/10.1155/2023/6647128 |
| spellingShingle | S. Akhlaghi M. Tavassoli Kajani M. Allame Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions Journal of Mathematics |
| title | Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions |
| title_full | Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions |
| title_fullStr | Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions |
| title_full_unstemmed | Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions |
| title_short | Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions |
| title_sort | numerical solution of fractional order integro differential equations via muntz orthogonal functions |
| url | http://dx.doi.org/10.1155/2023/6647128 |
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