Some Solutions of Hilfer Fractional Volterra Integral Equations by Using Pathway-Type Transform
International Journal of Mathematics and Mathematical Sciences, vol.2026, no.1, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1155/ijmm/1006382
- Journal Name: International Journal of Mathematics and Mathematical Sciences
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Middle East & Africa Database (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Hilfer fractional derivative, Pathway-type transform, Volterra integral equation
- Yıldız Technical University Affiliated: No
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.