Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation
Laplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8875792 |
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| _version_ | 1832546824500543488 |
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| author | Xiaoli Qiang Kamran Abid Mahboob Yu-Ming Chu |
| author_facet | Xiaoli Qiang Kamran Abid Mahboob Yu-Ming Chu |
| author_sort | Xiaoli Qiang |
| collection | DOAJ |
| description | Laplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to the real domain by analytic methods. Therefore, we need numerical methods to invert the solution to the real domain. In this work, we construct numerical schemes based on Laplace transform for the solution of fractional-order Volterra integrodifferential equations in the sense of the Atangana-Baleanu Caputo derivative. We propose two numerical methods for approximating the solution of fractional-order linear and nonlinear Volterra integrodifferential equations. In our scheme, the inverse Laplace transform is approximated using a contour integration method and Stehfest method. Some numerical experiments are performed to check the accuracy and efficiency of the methods. The results obtained using these methods are compared. |
| format | Article |
| id | doaj-art-9defffa8b9d24e13a45730d3cac327eb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9defffa8b9d24e13a45730d3cac327eb2025-02-03T06:46:58ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/88757928875792Numerical Approximation of Fractional-Order Volterra Integrodifferential EquationXiaoli Qiang0Kamran1Abid Mahboob2Yu-Ming Chu3Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Mathematics, Islamia College Peshawar, Khyber Pakhtoon Khwa, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaLaplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to the real domain by analytic methods. Therefore, we need numerical methods to invert the solution to the real domain. In this work, we construct numerical schemes based on Laplace transform for the solution of fractional-order Volterra integrodifferential equations in the sense of the Atangana-Baleanu Caputo derivative. We propose two numerical methods for approximating the solution of fractional-order linear and nonlinear Volterra integrodifferential equations. In our scheme, the inverse Laplace transform is approximated using a contour integration method and Stehfest method. Some numerical experiments are performed to check the accuracy and efficiency of the methods. The results obtained using these methods are compared.http://dx.doi.org/10.1155/2020/8875792 |
| spellingShingle | Xiaoli Qiang Kamran Abid Mahboob Yu-Ming Chu Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation Journal of Function Spaces |
| title | Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation |
| title_full | Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation |
| title_fullStr | Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation |
| title_full_unstemmed | Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation |
| title_short | Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation |
| title_sort | numerical approximation of fractional order volterra integrodifferential equation |
| url | http://dx.doi.org/10.1155/2020/8875792 |
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