An efficient approach for solving the Riccati equation with fractional orders

Authors:
Najeeb Alam Khan;Asmat Ara;Muhammad Jamil
Affiliations:
Department of Mathematics, University of Karachi, Karachi 75270, Pakistan;Department of Mathematics, University of Karachi, Karachi 75270, Pakistan;Abdul Salam School of Mathematical Sciences, GC University, Lahore, Pakistan and Department of Mathematics, NEDUET, Karachi-75270, Pakistan
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
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Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials

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Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation

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Abstract

The present study introduces a novel and simple analytical method for the solution of fractional order Riccati differential equation. In this approach, the solution considered as a Taylor series expansion converges rapidly to the nonlinear problem. New homotopy perturbation method (NHPM) depends only on two components of the homotopy series. The method is illustrated by applications and the results obtained are compared with those of the exact solution. Moreover, comparing the methodology with some known techniques shows that the present approach is relatively easy and efficient.