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New computational method for solving fractional Riccati equation. (English) Zbl 1427.35310

Summary: In this work, we implement the residual power series (RPS) method for solving the time fractional nonlinear Riccati initial value problem \[ \begin{cases} D^{\alpha}_t y(t)+a y(t)+b y^2(t)=c,\quad 0<\alpha \leq 1, \quad 0\leq t < R,\\ y(0)=d, \end{cases} \] 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.

MSC:

35R11 Fractional partial differential equations
35F25 Initial value problems for nonlinear first-order PDEs
35C10 Series solutions to PDEs
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