Operational Techniques for {}_pR_q Function via Integral Transforms and Fractional Calculus

This paper presents a comprehensive analysis of various integral transforms applied to the recently introduced {}_pR_q function, a generalization of the classical Mittag-Leffler-type functions. Due to their extended structure, these functions are significant in addressing complex problems across science, engineering, and technology. The study systematically investigates and derives the integral transforms of the {}_pR_q function, including the Laplace, Euler-Beta, Mellin, Mohand, Aboodh, SEE, Sadik, Whittaker, and K-transforms. In addition, the work establishes key operational properties such as n^{th} order fractional derivative formulas and recurrence relations. Lastly, we solve a fractional differential equations involving {}_pR_q functions as applications and develop its graphical representations.

کلیدواژه ها:

pRq function ، Integral Transform ، Generalized Mittag-Leffler function ، Generalized Wright function