Triangular functions for operational matrix of nonlinear fractional Volterra integral equations

摘要

We develop a new operational method based on triangular functions (TFs) to solve linear or nonlinear Volterra integral equations with weakly singular kernel. It operates with the TF-generalized operational matrix of integration, which can be an arbitrary and even fractional order. We provide the error and convergence analysis of the TF-approximation. Finally, to illustrate computational efficiency, we test the method for certain numerical examples with smooth, nonsmooth, and even singular kernels.