Analytical Evaluation of Fractional Calculus and Transforms Involving the Generalized Srivastava Triple Hypergeometric Function H_B,q,a^η,ξ

This work introduces a generalized version of Srivastava triple hypergeometric function HB(·) by incorporating the generalized Beta function Bq,aη,ξ(Φ1,Φ2) introduced by Oraby et al. [12]. We examine some analytical properties of the resulting generalized function, including various integral representations involving Exton's hypergeometric function, derivative properties, and classical integral transforms such as the Euler-Beta, Laplace, Mellin, and Whittaker transforms. We also explore the effects of Riemann-Liouville fractional integral and differential operators on the generalized Srivastava's function, yielding new insights in fractional calculus. Furthermore, we derive recurrence relations for further characterization. In addition, we present a numerical approximation table of HB,q,aη,ξ(·), computed using Wolfram Mathematica and computer algebraic software.