Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations
An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/2097317 |
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| _version_ | 1832549404587851776 |
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| author | Abdulnasir Isah Chang Phang Piau Phang |
| author_facet | Abdulnasir Isah Chang Phang Piau Phang |
| author_sort | Abdulnasir Isah |
| collection | DOAJ |
| description | An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations. |
| format | Article |
| id | doaj-art-c68eb5e39af94da68f4d990cba1b5b65 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-c68eb5e39af94da68f4d990cba1b5b652025-02-03T06:11:22ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/20973172097317Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph EquationsAbdulnasir Isah0Chang Phang1Piau Phang2Department of Mathematics, Ahmadu Bello University, Zaria, NigeriaDepartment of Mathematics and Statistics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Batu Pahat, MalaysiaFaculty of Computer Science and Information Technology, Universiti Malaysia Sarawak, Sarawak, MalaysiaAn effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations.http://dx.doi.org/10.1155/2017/2097317 |
| spellingShingle | Abdulnasir Isah Chang Phang Piau Phang Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations International Journal of Differential Equations |
| title | Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations |
| title_full | Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations |
| title_fullStr | Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations |
| title_full_unstemmed | Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations |
| title_short | Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations |
| title_sort | collocation method based on genocchi operational matrix for solving generalized fractional pantograph equations |
| url | http://dx.doi.org/10.1155/2017/2097317 |
| work_keys_str_mv | AT abdulnasirisah collocationmethodbasedongenocchioperationalmatrixforsolvinggeneralizedfractionalpantographequations AT changphang collocationmethodbasedongenocchioperationalmatrixforsolvinggeneralizedfractionalpantographequations AT piauphang collocationmethodbasedongenocchioperationalmatrixforsolvinggeneralizedfractionalpantographequations |