The Prabhakar fractional q-integral and q-differential operators, and their properties
In this paper, we have introduced the Prabhakar fractional q-integral and q-differential operators. We first study the semigroup property of the Prabhakar fractional q-integral operator, which allowed us to introduce the corresponding q-differential operator. Formulas for compositions of q-integral and q-differential operators are also presented. We show the boundedness of the Prabhakar fractional q-integral operator in the class of q-integrable functions.
Authors
- Serikbol Shaimardan (ORCID: https://orcid.org/0000-0002-0313-8457)
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Azizbek Mamanazarov (ORCID: https://orcid.org/0000-0001-8729-7852)
- Erkinjon Tulkinovich Karimov (ORCID: https://orcid.org/0000-0003-4443-6300)
Institutions
- HOGENT University of Applied Sciences and Arts (BE)
- Ghent University (BE)
- Ferghana State University (UZ)
Publication Details
- Journal
- Filomat
- Published
- 2025-01-01
- DOI
- https://doi.org/10.2298/fil2506003s
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fonds Wetenschappelijk Onderzoek
- Universiteit Gent
- Engineering and Physical Sciences Research Council
- Bijzonder Onderzoeksfonds UGent