On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative
Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM)...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/346089 |
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| _version_ | 1832548125830545408 |
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| author | Mehmet Merdan |
| author_facet | Mehmet Merdan |
| author_sort | Mehmet Merdan |
| collection | DOAJ |
| description | Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order 𝛼 are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivative |
| format | Article |
| id | doaj-art-7961eeb4586e426188868a00d0fb0d0b |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-7961eeb4586e426188868a00d0fb0d0b2025-02-03T06:42:11ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/346089346089On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville DerivativeMehmet Merdan0Department of Mathematics Engineering, Gümüşhane University, 29100 Gümüşhane, TurkeyFractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order 𝛼 are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivativehttp://dx.doi.org/10.1155/2012/346089 |
| spellingShingle | Mehmet Merdan On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative International Journal of Differential Equations |
| title | On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative |
| title_full | On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative |
| title_fullStr | On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative |
| title_full_unstemmed | On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative |
| title_short | On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative |
| title_sort | on the solutions fractional riccati differential equation with modified riemann liouville derivative |
| url | http://dx.doi.org/10.1155/2012/346089 |
| work_keys_str_mv | AT mehmetmerdan onthesolutionsfractionalriccatidifferentialequationwithmodifiedriemannliouvillederivative |