Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order
This manuscript is devoted to using Bernoulli polynomials to establish a new spectral method for computing the approximate solutions of initial and boundary value problems of variable-order fractional differential equations. With the help of the aforementioned method, some operational matrices of va...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/5/392 |
| _version_ | 1797600009478209536 |
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| author | Zareen A. Khan Sajjad Ahmad Salman Zeb Hussam Alrabaiah |
| author_facet | Zareen A. Khan Sajjad Ahmad Salman Zeb Hussam Alrabaiah |
| author_sort | Zareen A. Khan |
| collection | DOAJ |
| description | This manuscript is devoted to using Bernoulli polynomials to establish a new spectral method for computing the approximate solutions of initial and boundary value problems of variable-order fractional differential equations. With the help of the aforementioned method, some operational matrices of variable-order integration and differentiation are developed. With the aid of these operational matrices, the considered problems are converted to algebraic-type equations, which can be easily solved using computational software. Various examples are solved by applying the method described above, and their graphical presentation and accuracy performance are provided. |
| first_indexed | 2024-03-11T03:42:25Z |
| format | Article |
| id | doaj.art-32e5848e55fa4df4ae2506827c79c1d7 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:42:25Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-32e5848e55fa4df4ae2506827c79c1d72023-11-18T01:26:28ZengMDPI AGFractal and Fractional2504-31102023-05-017539210.3390/fractalfract7050392Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable OrderZareen A. Khan0Sajjad Ahmad1Salman Zeb2Hussam Alrabaiah3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhawa, Chakdara P.O. Box 18800, PakistanDepartment of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhawa, Chakdara P.O. Box 18800, PakistanCollege of Engineering, Al Ain University, Al Ain P.O. Box 64141, United Arab EmiratesThis manuscript is devoted to using Bernoulli polynomials to establish a new spectral method for computing the approximate solutions of initial and boundary value problems of variable-order fractional differential equations. With the help of the aforementioned method, some operational matrices of variable-order integration and differentiation are developed. With the aid of these operational matrices, the considered problems are converted to algebraic-type equations, which can be easily solved using computational software. Various examples are solved by applying the method described above, and their graphical presentation and accuracy performance are provided.https://www.mdpi.com/2504-3110/7/5/392fractional-order Bernoulli polynomialsoperational matricesvariable-order initial and boundary value problems |
| spellingShingle | Zareen A. Khan Sajjad Ahmad Salman Zeb Hussam Alrabaiah Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order Fractal and Fractional fractional-order Bernoulli polynomials operational matrices variable-order initial and boundary value problems |
| title | Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order |
| title_full | Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order |
| title_fullStr | Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order |
| title_full_unstemmed | Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order |
| title_short | Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order |
| title_sort | bernoulli type spectral numerical scheme for initial and boundary value problems with variable order |
| topic | fractional-order Bernoulli polynomials operational matrices variable-order initial and boundary value problems |
| url | https://www.mdpi.com/2504-3110/7/5/392 |
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