Triangular functions for operational matrix of nonlinear fractional Volterra integral equations (Q499984)

The authors consider a numerical method for solving the Volterra equation \[ f(t) - \lambda \int_0^t (t-\tau)^{\alpha-1} k(t, \tau) F(f(\tau)) d \tau = g(t) \] with a given \(\alpha > 0\). Although the problem is originally formulated for a general nonlinearity \(F\), it is actually only tackled for \(F(z) = z^n\) with some \(n \in \mathbb N\). The method is based on a piecewise linear interpolation of the unknown function \(f\). The authors give the formulas that can be used to compute the numerical solution and a few numerical examples, but no theoretical analysis of the integral equation solving algorithm.