Loh, Jian Rong (2018) Efficient schemes on solving fractional integro-differential equations. Doctoral thesis, Universiti Tun Hussein Onn Malaysia.
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Abstract
Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for the
| Item Type: | Thesis (Doctoral) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Applied Science and Technology > Department of Mathematics and Statistics |
| Depositing User: | Mrs. Sabarina Che Mat |
| Date Deposited: | 06 Jul 2021 08:22 |
| Last Modified: | 06 Jul 2021 08:22 |
| URI: | http://eprints.uthm.edu.my/id/eprint/204 |
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