IJPAM: Volume 106, No. 1 (2016)

FRACTIONAL POLYNOMIAL METHOD FOR SOLVING
FRACTIONAL ORDER RICCATI DIFFERENTIAL EQUATION

K. Krishnaveni$^1$, K. Kannan$^2$, S. Raja Balachandar$^3$
$^{1,2,3}$Department of Mathematics
School of Humanities and Sciences
SASTRA University,Thanjavur, INDIA


Abstract. The aim of this article is to present the fractional shifted Legendre polynomial method to solve the Riccati differential equation of fractional order. The properties of shifted Legendre polynomials together with the Caputo fractional derivative are used to reduce the problem to the solution of algebraic equations. A new theoretical analysis such as convergence analysis and error bound for the proposed technique has been demonstrated. The obtained results reveal that the performance of the proposed method is very accurate and reliable.

Received: September 7, 2015

AMS Subject Classification: 65Lxx, 47E05, 34Lxx

Key Words and Phrases: fractional Riccati differential equation, fractional shifted Legendre polynomial method, Caputo fractional derivative, nonlinear differential equation

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DOI: 10.12732/ijpam.v106i1.21 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 273 - 278


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