An algorithm for the numerical solution of differential equations of fractional order
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.
scientific article; zbMATH DE number 1128742