New computational method for solving fractional Riccati equation


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.


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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


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