Some Solutions of Hilfer Fractional Volterra Integral Equations by Using Pathway-Type Transform

Faten H. Damag, Mohammad Alshammari, Amin Saif, Mohammed S. Alsharafi and Adem Kilicman

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-15

Abstract: The Pathway-type Pε-transform technique has been introduced as a versatile binomial transform encompassing various classes, including the classical Laplace transform. In this paper, we apply this technique to derive solutions for fractional Volterra integral equations (FVIEs) and fractional Abel–Volterra integral equations (FAVIEs) that involve Hilfer fractional derivatives. We establish the existence of solutions for several systems, a system of FVIEs, a system of FAVIEs, and a mixed system combining Volterra integral equations with FAVIEs. Additionally, we present a numerical and graphical analysis of these solutions, illustrating their behavior and properties.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1006382

DOI: 10.1155/ijmm/1006382

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