Generalized Extended Riemann-Liouville Type Fractional Derivative Operator
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Authors: H. ABBAS, A. AZZOUZ, M. B. ZAHAF AND M. BELMEKKI
DOI: 10.46793/KgJMat2301.057A
Abstract:
In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform and integral representations are obtained for these generalizations. Further, an extension of the Riemann-Liouville fractional derivative operator is established.
Keywords:
Generalized extended incomplete gamma function, generalized extended beta function, extended Riemann-Liouville fractional derivative, Mellin transform, extended Gauss hypergeometric function, integral representation.
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