Diethelm, Kai An algorithm for the numerical solution of differential equations of fractional order. (English) Zbl 0890.65071 ETNA, Electron. Trans. Numer. Anal. 5, 1-6 (1997). 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) Cited in 3 ReviewsCited in 220 Documents MSC: 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 Keywords:fractional differential equation; Riemann-Liouville fractional derivative; numerical examples; error estimates; implicit algorithm PDF BibTeX XML Cite \textit{K. Diethelm}, ETNA, Electron. Trans. Numer. Anal. 5, 1--6 (1997; Zbl 0890.65071) Full Text: EuDML EMIS OpenURL