A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms

The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that pro...

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Veröffentlicht in:Journal of Mathematics Jg. 2022; H. 1
Hauptverfasser: Palsaniya, Vandana, Mittal, Ekta, Suthar, D. L., Joshi, Sunil
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cairo Hindawi 2022
John Wiley & Sons, Inc
Wiley
Schlagworte:
Applied mathematics
Derivatives
Fractional calculus
Hypergeometric functions
Integral transforms
Integrals
Laplace transforms
Mathematical functions
Mathematics
Operators (mathematics)
Partial differential equations
Theorems
ISSN:2314-4629, 2314-4785
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Zusammenfassung:The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas.
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ISSN:2314-4629
2314-4785
DOI:10.1155/2022/5343801