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A -Weyl fractional operator of the extended -type function in a complex domain
Sarem H Hadi1,2, Khalid A Challab3, Ali Hasan Ali1,4
1Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
Methodsx
|December 17, 2024
Summary
This study introduces the novel q-function, an extension of the q-special function, exploring its analytical properties and applications in fractional calculus. The research details derivative and integral formulas, and a q-Weyl fractional integral operator.
Area of Science:
- Mathematical Analysis
- Special Functions
- Fractional Calculus
Background:
- The study builds upon the foundation of well-known q-special functions.
- It draws inspiration from the fundamental properties of the exponential function.
- Existing analytical tools are extended to explore new mathematical constructs.
Purpose of the Study:
- To introduce and define a new mathematical entity: the q-function.
- To investigate the analytical properties of the q-function, including its derivatives and integrals.
- To explore applications of the q-function within the domain of fractional calculus, specifically using a q-Weyl fractional integral operator.
Main Methods:
- Introduction of the q-function based on the exponential function.
- Application of differential and integral operators to analyze the q-function.
- Development and study of a q-Weyl fractional integral operator involving the q-function, utilizing a novel q-differential operator.
Main Results:
- The paper provides a formal definition of the q-function.
- Key derivative and integral formulas for the q-function are derived and presented.
- An investigation into the application of the q-Weyl fractional integral operator associated with the q-function is conducted.
Conclusions:
- The q-function is successfully introduced and its fundamental analytical properties are established.
- The study demonstrates the utility of the q-function in the context of fractional integral operators.
- This work expands the landscape of special functions and their applications in mathematical analysis.
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