Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative
In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical expressions of the expansion coefficient ck by Bernoulli polynomials approximation have been derived for both...
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2019
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| Online Access: | http://eprints.uthm.edu.my/4194/1/AJ%202019%20%28247%29.pdf http://eprints.uthm.edu.my/4194/ https://doi.org/10.1007/s00009-019-1300-7 |
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| _version_ | 1833417535262818304 |
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| author | Loh, Jian Rong Phang, Chang |
| author_facet | Loh, Jian Rong Phang, Chang |
| author_sort | Loh, Jian Rong |
| building | UTHM Library |
| collection | Institutional Repository |
| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical expressions of the expansion coefficient ck by Bernoulli polynomials approximation have been derived for both approximation of single- and double-variable function. The Bernoulli polynomials operational matrix of right-sided Caputo’s fractional derivative Pα −;B is derived. By approximating each term in the Fredholm FIDE with right-sided Caputo’s fractional derivative in terms of Bernoulli polynomials basis, the equation is reduced to a system of linear algebraic equation of the unknown coefficients ck. Solving for the coefficients produces the approximate solution for this special type of FIDE. |
| format | Article |
| id | my.uthm.eprints-4194 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2019 |
| publisher | Springer |
| record_format | eprints |
| spelling | my.uthm.eprints-41942021-11-28T07:24:15Z http://eprints.uthm.edu.my/4194/ Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative Loh, Jian Rong Phang, Chang QA299.6-433 Analysis In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical expressions of the expansion coefficient ck by Bernoulli polynomials approximation have been derived for both approximation of single- and double-variable function. The Bernoulli polynomials operational matrix of right-sided Caputo’s fractional derivative Pα −;B is derived. By approximating each term in the Fredholm FIDE with right-sided Caputo’s fractional derivative in terms of Bernoulli polynomials basis, the equation is reduced to a system of linear algebraic equation of the unknown coefficients ck. Solving for the coefficients produces the approximate solution for this special type of FIDE. Springer 2019 Article PeerReviewed text en http://eprints.uthm.edu.my/4194/1/AJ%202019%20%28247%29.pdf Loh, Jian Rong and Phang, Chang (2019) Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative. Mediterranean Journal Of Mathematics, 16 (28). pp. 1-25. ISSN 1660-5446 https://doi.org/10.1007/s00009-019-1300-7 |
| spellingShingle | QA299.6-433 Analysis Loh, Jian Rong Phang, Chang Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title | Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title_full | Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title_fullStr | Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title_full_unstemmed | Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title_short | Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| title_sort | numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative |
| topic | QA299.6-433 Analysis |
| url | http://eprints.uthm.edu.my/4194/1/AJ%202019%20%28247%29.pdf http://eprints.uthm.edu.my/4194/ https://doi.org/10.1007/s00009-019-1300-7 |
| url_provider | http://eprints.uthm.edu.my/ |