On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2012 Turkey English Publisher:Hindawi LimitedJournal:International Journal of Differential Equations, volume 2,012, pages 1-17 (issn: 1687-9643, eissn: 1687-9651,

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Authors: Merdan, Mehmet;

doi: 10.1155/2012/346089

handle: 20.500.12440/2986

On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

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Abstract

Summary: 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 \(\alpha\) 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.

Country

Turkey

Related Organizations

Gümüşhane University
Turkey
Üniversite ve Araştırma Kütüphanecileri Derneği
Turkey

Keywords

fractional variational iteration method, modified Riemann-Liouville derivative, QA1-939, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Fractional ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Mathematics, Theoretical approximation of solutions to ordinary differential equations

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