Some Fractional Calculus Results Based on Extended Gauss Hypergeometric Functions and Integral Transform


Sunil Kumar Sharma,Ashok Singh Shekhawat,



Gamma function,Extended generalized beta functions,Generalized hypergeometric functions,Extended generalized hypergeometric functions,Fractional integral operators,Integral transforms,Pathway fractional integral operator,


Extensions of number of well-known special function such as Beta and Gauss hypergeometric and their properties have been investigated recently by several authors. Our approach is based on the use of Generalized Fractional Calculus (GFC) operators. We aim to investigate the MSM (Marichev-Saigo-Maeda) fractional calculus operator, Caputo-type MSM-fractional differential operator and pathway fractional integral operator of the extended generalized Gauss hypergeometric function. Furthermore, by employing some integral transform on the resulting formulas, we presented some more image formulas. All the results derived here are of general character and can yield a number of (known and new) results in theory of special functions.


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