New computational method for solving fractional Riccati equation
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Authors
Mohammed Ali
- Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan.
Imad Jaradat
- Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan.
Marwan Alquran
- Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan.
Abstract
In this work, we implement the residual power series (RPS) method for solving the time fractional nonlinear Riccati initial
value problem
\[
\begin{cases}
D^{\alpha}_t y(t)+a y(t)+b y^2(t)=c,\,\,\,\,\,0<\alpha \leq 1, \,0\leq t < R,\\
y(0)=d,
\end{cases}
\]
where \(a, b, c, d\) are constants and \(D^\alpha_t\)
is the Caputo fractional derivative. An analytical solution of \(y(t)\) is obtained as a convergent
fractional power series in \(t\). To demonstrate the dependability of the proposed method, three illustrative examples are offered and
the obtained results are compared with some existing results in the literature. Moreover, the results show that the approximate
solutions are continuously communicate, as \(\alpha \) increases, until the first derivative is reached.
Share and Cite
ISRP Style
Mohammed Ali, Imad Jaradat, Marwan Alquran, New computational method for solving fractional Riccati equation, Journal of Mathematics and Computer Science, 17 (2017), no. 1, 106-114
AMA Style
Ali Mohammed, Jaradat Imad, Alquran Marwan, New computational method for solving fractional Riccati equation. J Math Comput SCI-JM. (2017); 17(1):106-114
Chicago/Turabian Style
Ali, Mohammed, Jaradat, Imad, Alquran, Marwan. "New computational method for solving fractional Riccati equation." Journal of Mathematics and Computer Science, 17, no. 1 (2017): 106-114
Keywords
- Fractional Riccati
- Caputo derivative
- residual power series.
MSC
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