International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 129-143
doi:10.1155/S016117120201325X

Singularly perturbed Volterra integral equations with weakly singular kernels

Abstract

We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the paper demonstrates the similarity that these solutions have to a special function called the Mittag-Leffler function.