Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique
Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) with Caputo’s derivative (CD) are numerically solved...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/170 |
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| author | Ghazala Akram Muhammad Abbas Hira Tariq Maasoomah Sadaf Thabet Abdeljawad Manar A. Alqudah |
| author_facet | Ghazala Akram Muhammad Abbas Hira Tariq Maasoomah Sadaf Thabet Abdeljawad Manar A. Alqudah |
| author_sort | Ghazala Akram |
| collection | DOAJ |
| description | Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) with Caputo’s derivative (CD) are numerically solved using a sextic polynomial spline technique (SPST). These equations are frequently applied in a wide variety of real-world applications, such as strain gradient elasticity, phase separation in binary mixtures, and modelling of thin beams and plates, all of which are key parts of mechanical engineering. The SPST can be used for space discretization, whereas the backward Euler formula can be used for time discretization. For the temporal discretization, the method’s convergence and stability are assessed. To show the accuracy and applicability of the proposed technique, numerical simulations are employed. |
| first_indexed | 2024-03-09T19:49:49Z |
| format | Article |
| id | doaj.art-ffc25274c1524b1299a435dbe50b00ea |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:49Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-ffc25274c1524b1299a435dbe50b00ea2023-11-24T01:14:50ZengMDPI AGFractal and Fractional2504-31102022-03-016317010.3390/fractalfract6030170Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline TechniqueGhazala Akram0Muhammad Abbas1Hira Tariq2Maasoomah Sadaf3Thabet Abdeljawad4Manar A. Alqudah5Department of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, Government College Women University, Sialkot 51310, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDeveloping mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) with Caputo’s derivative (CD) are numerically solved using a sextic polynomial spline technique (SPST). These equations are frequently applied in a wide variety of real-world applications, such as strain gradient elasticity, phase separation in binary mixtures, and modelling of thin beams and plates, all of which are key parts of mechanical engineering. The SPST can be used for space discretization, whereas the backward Euler formula can be used for time discretization. For the temporal discretization, the method’s convergence and stability are assessed. To show the accuracy and applicability of the proposed technique, numerical simulations are employed.https://www.mdpi.com/2504-3110/6/3/170higher-order partial differential equations (PDEs)evolution problemsCaputo time fractional derivativesextic spline polynomialscollocation method |
| spellingShingle | Ghazala Akram Muhammad Abbas Hira Tariq Maasoomah Sadaf Thabet Abdeljawad Manar A. Alqudah Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique Fractal and Fractional higher-order partial differential equations (PDEs) evolution problems Caputo time fractional derivative sextic spline polynomials collocation method |
| title | Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique |
| title_full | Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique |
| title_fullStr | Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique |
| title_full_unstemmed | Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique |
| title_short | Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique |
| title_sort | numerical approximations for the solutions of fourth order time fractional evolution problems using a novel spline technique |
| topic | higher-order partial differential equations (PDEs) evolution problems Caputo time fractional derivative sextic spline polynomials collocation method |
| url | https://www.mdpi.com/2504-3110/6/3/170 |
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