Some fractional calculus findings associated with the incomplete I-functions

In this article, several interesting properties of the incomplete I -functions associated with the Marichev–Saigo–Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I -functions increases about the utilization of the above-mentioned operat...

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Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 24
Main Authors: Jangid, Kamlesh, Bhatter, Sanjay, Meena, Sapna, Baleanu, Dumitru, Al Qurashi, Maysaa, Purohit, Sunil Dutt
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 04.06.2020
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Difference and Functional Equations
Fractional calculus
Fractional calculus operators
Functional Analysis
Incomplete gamma functions
Incomplete I-functions
Mathematics
Mathematics and Statistics
Mellin–Barnes type contour
Methods
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Topics in Special Functions and q-Special Functions: Theory
Incomplete
functions
33E20
33B20
Fractional calculus operators
Mellin–Barnes type contour
26A33
Incomplete gamma functions
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:In this article, several interesting properties of the incomplete I -functions associated with the Marichev–Saigo–Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I -functions increases about the utilization of the above-mentioned operators toward the power multiple of the incomplete I -functions. Further, the Caputo-type MSM fractional order differentiation for the incomplete I -functions is studied and investigated. Saigo, Riemann–Liouville, and Erdélyi–Kober fractional operators are also discussed as specific cases.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02725-7