An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method
An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2018/7237680 |
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| author | Rezvan Ghoochani-Shirvan Jafar Saberi-Nadjafi Morteza Gachpazan |
| author_facet | Rezvan Ghoochani-Shirvan Jafar Saberi-Nadjafi Morteza Gachpazan |
| author_sort | Rezvan Ghoochani-Shirvan |
| collection | DOAJ |
| description | An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on. |
| format | Article |
| id | doaj-art-11c09fe3628e428aad7b6cec0efd3ddf |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-11c09fe3628e428aad7b6cec0efd3ddf2025-02-03T06:13:12ZengWileyInternational Journal of Differential Equations1687-96431687-96512018-01-01201810.1155/2018/72376807237680An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform MethodRezvan Ghoochani-Shirvan0Jafar Saberi-Nadjafi1Morteza Gachpazan2Department of Applied Mathematics, Ferdowsi University of Mashhad, International Campus, Mashhad, IranDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranAn analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on.http://dx.doi.org/10.1155/2018/7237680 |
| spellingShingle | Rezvan Ghoochani-Shirvan Jafar Saberi-Nadjafi Morteza Gachpazan An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method International Journal of Differential Equations |
| title | An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method |
| title_full | An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method |
| title_fullStr | An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method |
| title_full_unstemmed | An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method |
| title_short | An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method |
| title_sort | analytical and approximate solution for nonlinear volterra partial integro differential equations with a weakly singular kernel using the fractional differential transform method |
| url | http://dx.doi.org/10.1155/2018/7237680 |
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