The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations
The Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to solve the corresponding Volterra integral equation of the given...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/21/3388 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850193417268625408 |
|---|---|
| author | Haifa Bin Jebreen Ioannis Dassios |
| author_facet | Haifa Bin Jebreen Ioannis Dassios |
| author_sort | Haifa Bin Jebreen |
| collection | DOAJ |
| description | The Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to solve the corresponding Volterra integral equation of the given equation. In the employed method, the derivative and fractional integral operators are expressed in the Chebyshev cardinal functions, which reduce the computational load. The method is characterized by its simplicity, adherence to boundary conditions, and high accuracy. An exact analysis has been provided to demonstrate the convergence of the scheme, and illustrative examples validate our investigation. |
| format | Article |
| id | doaj-art-0dcacaae0bbf4f4fa698d37e669ca258 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-0dcacaae0bbf4f4fa698d37e669ca2582025-08-20T02:14:16ZengMDPI AGMathematics2227-73902024-10-011221338810.3390/math12213388The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential EquationsHaifa Bin Jebreen0Ioannis Dassios1Department of mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFaculty of Engineering, Aristotle University of Thessaloniki, 541 24 Thessaloniki, GreeceThe Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to solve the corresponding Volterra integral equation of the given equation. In the employed method, the derivative and fractional integral operators are expressed in the Chebyshev cardinal functions, which reduce the computational load. The method is characterized by its simplicity, adherence to boundary conditions, and high accuracy. An exact analysis has been provided to demonstrate the convergence of the scheme, and illustrative examples validate our investigation.https://www.mdpi.com/2227-7390/12/21/3388Chebyshev cardinal functionsLobatto griddelay differential equationscollocation method |
| spellingShingle | Haifa Bin Jebreen Ioannis Dassios The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations Mathematics Chebyshev cardinal functions Lobatto grid delay differential equations collocation method |
| title | The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations |
| title_full | The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations |
| title_fullStr | The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations |
| title_full_unstemmed | The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations |
| title_short | The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations |
| title_sort | collocation method based on the new chebyshev cardinal functions for solving fractional delay differential equations |
| topic | Chebyshev cardinal functions Lobatto grid delay differential equations collocation method |
| url | https://www.mdpi.com/2227-7390/12/21/3388 |
| work_keys_str_mv | AT haifabinjebreen thecollocationmethodbasedonthenewchebyshevcardinalfunctionsforsolvingfractionaldelaydifferentialequations AT ioannisdassios thecollocationmethodbasedonthenewchebyshevcardinalfunctionsforsolvingfractionaldelaydifferentialequations AT haifabinjebreen collocationmethodbasedonthenewchebyshevcardinalfunctionsforsolvingfractionaldelaydifferentialequations AT ioannisdassios collocationmethodbasedonthenewchebyshevcardinalfunctionsforsolvingfractionaldelaydifferentialequations |