Generalized Extended Riemann-Liouville Type Fractional Derivative Operator

Hafida Abbas, Abdelhalim Azzouz, Mohammed Brahim Zahaf, Mohammed Belmekki

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 [4]. 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.