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.

No abstract

No abstract

The additive decomposition singular perturbation method and the theory of fractional integration are used to study asymptotic solutions of singularly perturbed Volterra integrodifferential equations with kernels having integrable singularity. The validity of the approximation is also demonstrated