Pathway integral operator involving (P, Q) extended Struve function and its applications

This paper's goal is to prove two theorems utilizing the generalized Struve function and the pathway fractional integral operator via Struve function. Our findings are rather universal. Here are a few exceptional examples as well. Over the past few years, fractional calculus has drawn increased attention because of its efficiency and possible applications to a wide range of mathematical and statistical problems. The pathway fractional operator representations of different special functions, including the Bessel function, extended Bessel functions, Struve function, and generalized Struve function, have been examined by a number of writers. Numerous scholars have demonstrated the importance of the Struve function and its careful examination in the theory of special functions for investigating generalization and certain applications. Additionally, we develop the pathway fractional integration of cosine, hyperbolic cosine, sine, and hyperbolic sine functions and provide the relationship between the trigonometric function and the (P, Q) - Struve function. In order to derive the pathway integral representation of the classical Struve function, a few special cases were also established. It is noted that the primary findings here are sufficiently generic to allow for specialization to produce a large number of known and (probably) novel discoveries. Our findings will contribute to the extension of certain classical statistical distributions to broader distribution classes, which will be helpful in real-world scenarios.