International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 129-143
Singularly perturbed Volterra integral equations with
weakly singular kernels
1Department of Mathematics, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania
2Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
Received 9 May 2001; Revised 25 September 2001
Copyright © 2002 Angelina Bijura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.