  In this paper, we aim to 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.
