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Singularly perturbed Volterra integral equations with weakly singular kernels

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  • Angelina Bijura

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.

Suggested Citation

  • Angelina Bijura, 2002. "Singularly perturbed Volterra integral equations with weakly singular kernels," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:815890
    DOI: 10.1155/S016117120201325X
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    Cited by:

    1. Yapman, Ömer & Amiraliyev, Gabil M., 2021. "Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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