$\left(p,q\right)$-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 ⋅ in the kernel due to Marichev–Saigo–Maeda are applied to the p , q -extended Struve function. The results are stated in terms of Hadamard product of the Fox–Wright function ψ r s z and the p , q -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 p , q -extended Struve function. Technique and findings can be implemented and applied to a number of similar fractional problems in applied mathematics and physics.

Application of the Pathway-Type Transform to a New Form of a Fractional Kinetic Equation Involving the Generalized Incomplete Wright Hypergeometric Functions

“…Because of the usefulness and great importance of the kinetic equation in some astrophysical issues, fractional kinetic equations have been investigated to describe the various phenomena governed by anomalous reactions in dynamical systems [6][7][8][9]. Several authors have recently presented solutions to various families of fractional kinetic equations involving special functions using the Laplace transform, Sumudu transform, Prabhakar-type operators, Hadamard fractional integrals, and pathway-type transform based on these principles (see, for example, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]).…”

“…Many generalizations and solutions of the fractional-order kinetic equation have recently been developed, utilizing a variety of fractional integral transforms including the fractional Laplace transform [12][13][14][15][16], fractional Sumudu transform [17][18][19], Hadamard fractional integrals [20][21][22], fractional pathway transform [23,24] and Prabhakar-type operators [25], which have been extensively studied. In particular, Khan et al [14] presented solutions for fractional kinetic equations associated with the (p, q)-extended τhypergeometric and confluent hypergeometric functions using the Laplace transform, while Hidan et al [15] discussed a technique for the Laplace transformation of solutions of fractional kinetic equations involving extended (k, t)-Gauss hypergeometric matrix functions.…”

Solutions to Fractional q-Kinetic Equations Involving Quantum Extensions of Generalized Hyper Mittag-Leffler Functions

“…Also, several ways to study the extension and development of fractional kinetic equations involving various special functions have been presented. For example, we refer to contemporary works by Agarwal et al [9], Saxena et al [10], Akel et al [11], Hidan et al [12], Almalkia and Abdalla [13], Kolokoltsov and Troeva [14], Habenom et al [15] and Abdalla and Akel [16].…”

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

“…Readers can refer to [13][14][15][16][17][18][19][20] for more generalizations and extensions of extended fractional kinetic equations.…”