Geodesic
Generalized Extended Riemann-Liouville Type Fractional Derivative Operator
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 1, p. 57 .

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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.
DOI : 10.46793/KgJMat2301.057A
Classification : 26A33, 33B15, 33B20, 33C20, 33C65
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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Hafida Abbas; Abdelhalim Azzouz; Mohammed Brahim Zahaf; Mohammed Belmekki. Generalized Extended Riemann-Liouville Type Fractional Derivative Operator. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 1, p. 57 . doi : 10.46793/KgJMat2301.057A. http://geodesic.mathdoc.fr/articles/10.46793/KgJMat2301.057A/

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