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

The author considers the fractional differential equation \[ (D^q[x-x_0])(t)=\beta x(t)+f(t), \qquad 0\leq t \leq 1, \quad x(0)=x_0, \] where \(0<q<1\), \(f\) is a given function on the interval \([0,1]\), \(\beta \leq 0\). 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.
Reviewer: S.Yanchuk (Kyïv)


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L70 Error bounds for numerical methods for ordinary differential equations
26A33 Fractional derivatives and integrals
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