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An algorithm for the numerical solution of differential equations of fractional order. (English) Zbl 0890.65071
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.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L70Error bounds (numerical methods for ODE)
26A33Fractional derivatives and integrals (real functions)
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