p , q -Extended Struve Function: Fractional Integrations and Application to Fractional Kinetic Equations

Abstract

In this paper, the generalized fractional integral operators involving Appell’s function $F_3\left(\cdot \right)$ in the kernel due to Marichev–Saigo–Maeda are applied to the $\left(p,q\right)$ -extended Struve function. The results are stated in terms of Hadamard product of the Fox–Wright function ${{\displaystyle {}_r\psi }}_s\left(z\right)$ and the $\left(p,q\right)$ -extended Gauss hypergeometric function. A few of the special cases (Saigo integral operators) of our key findings are also reported in the corollaries. In addition, the solutions of a generalized fractional kinetic equation employing the concept of Laplace transform are also obtained and examined as an implementation of the $\left(p,q\right)$ -extended Struve function. Technique and findings can be implemented and applied to a number of similar fractional problems in applied mathematics and physics.