The Prabhakar fractional q-integral and q-differential operators, and their properties

2022/12/17 by Serikbol Shaimardan, Erkinjon Karimov, Shaimardan, Serikbol +5
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2212.08843

openalex publication_date 2022/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we have introduced the Prabhakar fractional q-integral and q-differential operators. We first study the semi-group 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.

Related

• Study of new class of q-fractional integral operator
• Certain fractional q -integrals and q -derivatives
• On q-fractional derivatives of Riemann--Liouville and Caputo type
• Study of new class of q-fractional derivative and its properties
• On extension of the _rR_s,q(α,β,z) function and their q-calculus