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Fractional Calculus of the Generalized Mittag-Leffler Type Function
1Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342005, India.
International Scholarly Research Notices
|July 21, 2016
Summary
This study introduces the R-function, an extension of the generalized Mittag-Leffler function. We establish its relationship with Saigo fractional calculus operators, generalizing prior findings.
Area of Science:
- Fractional Calculus
- Special Functions
Background:
- The generalized Mittag-Leffler function is a key special function in fractional calculus.
- Existing literature explores relationships between special functions and fractional calculus operators.
Purpose of the Study:
- Introduce and analyze a novel R-function.
- Investigate the connections between the R-function and Saigo fractional calculus operators.
Main Methods:
- Definition of the R-function.
- Derivation of relationships using properties of fractional calculus operators.
- Comparison with existing results in the literature.
Main Results:
- The R-function is defined as an extension of the generalized Mittag-Leffler function.
- New relations are established between the R-function and Saigo fractional calculus operators.
- Previously published results by Samko et al., Kilbas, and Sharma & Jain are shown to be special cases.
Conclusions:
- The R-function offers a new perspective in the study of special functions within fractional calculus.
- The derived relations provide a unified framework for certain fractional calculus results.
- This work extends the understanding of the interplay between special functions and fractional operators.
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