TY - JOUR
T1 - A Collocation Method for Solving Fractional Riccati Differential Equation
AU - Gülsu , Mustafa
AU - Öztürk , Yalçın
AU - Anapali , Ayşe
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 872
EP - 884
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.12-m12118
UR - https://global-sci.org/intro/article_detail/aamm/101.html
KW - Riccati equation, fractional derivative, collocation method, generalized Taylor series, approximate solution.
AB - <p style="text-align: justify;">In this article, we have introduced a Taylor collocation method,
which is based on collocation method for solving fractional Riccati
differential equation. The fractional derivatives are described in
the Caputo sense. This method is based on first taking the truncated
Taylor expansions of the solution function in the fractional Riccati
differential equation and then substituting their matrix forms into
the equation. Using collocation points, the systems of nonlinear
algebraic equation are derived. We further solve the system of
nonlinear algebraic equation using Maple 13 and thus obtain the
coefficients of the generalized Taylor expansion. Illustrative
examples are presented to demonstrate the effectiveness of the
proposed method.</p>