An efficient spline technique for solving time-fractional integro-differential equations
Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability to approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal of this study is to use extended cubic...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023065155 |
| _version_ | 1797669902390132736 |
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| author | Muhammad Abbas Sadia Aslam Farah Aini Abdullah Muhammad Bilal Riaz Khaled A. Gepreel |
| author_facet | Muhammad Abbas Sadia Aslam Farah Aini Abdullah Muhammad Bilal Riaz Khaled A. Gepreel |
| author_sort | Muhammad Abbas |
| collection | DOAJ |
| description | Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability to approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal of this study is to use extended cubic B-spline (ExCuBS) functions with a new second order derivative approximation to obtain the numerical solution of the weakly singular kernel (SK) non-linear fractional partial integro-differential equation (FPIDE). The spatial and temporal fractional derivatives are discretized by ExCuBS and the Caputo finite difference scheme, respectively. The present study found that it is stable and convergent. The validity of the current approach is examined on a few test problems, and the obtained outcomes are compared with those that have previously been reported in the literature. |
| first_indexed | 2024-03-11T20:51:36Z |
| format | Article |
| id | doaj.art-63b709ae81c747f79fffd9a1a59fd263 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-11T20:51:36Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-63b709ae81c747f79fffd9a1a59fd2632023-10-01T05:59:09ZengElsevierHeliyon2405-84402023-09-0199e19307An efficient spline technique for solving time-fractional integro-differential equationsMuhammad Abbas0Sadia Aslam1Farah Aini Abdullah2Muhammad Bilal Riaz3Khaled A. Gepreel4Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan; Corresponding author.Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaDepartment of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon; Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza, 11/1280-233 Gdańsk, Poland; Department of Mathematics, University of Management and Technology, 54770 C-II Johar Town Lahore, Pakistan; Corresponding author at: Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza, 11/1280-233 Gdańsk, Poland.Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaSpline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability to approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal of this study is to use extended cubic B-spline (ExCuBS) functions with a new second order derivative approximation to obtain the numerical solution of the weakly singular kernel (SK) non-linear fractional partial integro-differential equation (FPIDE). The spatial and temporal fractional derivatives are discretized by ExCuBS and the Caputo finite difference scheme, respectively. The present study found that it is stable and convergent. The validity of the current approach is examined on a few test problems, and the obtained outcomes are compared with those that have previously been reported in the literature.http://www.sciencedirect.com/science/article/pii/S2405844023065155ApproximationExCuBSFractional order partial integro-differential equationCaputo's fractional derivativeFinite difference schemeStability and convergence |
| spellingShingle | Muhammad Abbas Sadia Aslam Farah Aini Abdullah Muhammad Bilal Riaz Khaled A. Gepreel An efficient spline technique for solving time-fractional integro-differential equations Heliyon Approximation ExCuBS Fractional order partial integro-differential equation Caputo's fractional derivative Finite difference scheme Stability and convergence |
| title | An efficient spline technique for solving time-fractional integro-differential equations |
| title_full | An efficient spline technique for solving time-fractional integro-differential equations |
| title_fullStr | An efficient spline technique for solving time-fractional integro-differential equations |
| title_full_unstemmed | An efficient spline technique for solving time-fractional integro-differential equations |
| title_short | An efficient spline technique for solving time-fractional integro-differential equations |
| title_sort | efficient spline technique for solving time fractional integro differential equations |
| topic | Approximation ExCuBS Fractional order partial integro-differential equation Caputo's fractional derivative Finite difference scheme Stability and convergence |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023065155 |
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