The Prabhakar fractional q-integral and q-differential operators, and their properties
Serikbol ShaimardanDepartment of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Building Ghent, BelgiumErkinjon KarimovDepartment of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Building Ghent, BelgiumMichael RuzhanskyDepartment of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Building Ghent, BelgiumAzizbek MamanazarovFergana State University, Fergana, Uzbekistan
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Аннотация
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.
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