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Zbl 0890.65071
Diethelm, Kai
An algorithm for the numerical solution of differential equations of fractional order. (English)
[J] ETNA, Electron. Trans. Numer. Anal. 5, 1-6 (1997). ISSN 1068-9613/e

The author considers the fractional differential equation $$ (D^q[x-x_0])(t)=\beta x(t)+f(t), \qquad 0\le t \le 1, \quad x(0)=x_0,$$ where $0<q<1$, $f$ is a given function on the interval $[0,1]$, $\beta \le 0$. Here $D^q x$ denotes the Riemann-Liouville fractional derivative of order $q$. An implicit algorithm for the approximate solution of an important class of these equations is proposed. Error estimates and numerical examples are given.
[S.Yanchuk (Ky\" iv)]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L70 Error bounds (numerical methods for ODE)
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional differential equation; Riemann-Liouville fractional derivative; numerical examples; error estimates; implicit algorithm

Cited in: Zbl 0958.65081 Zbl 0926.65070

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Zentralblatt MATH Berlin [Germany]