SOME MATRIX FAMILIES OF THE HURWITZ–LERCH Ζ-Functions AND ASSOCIATED FRACTIONAL KINETIC EQUATIONS

Abstract

This research paper aims to introduce an extension of the [Formula: see text]-Hurwitz–Lerch [Formula: see text]-function of matrix arguments and interpret its several properties, like generating matrix relations, derivative formulae, Mellin transforms and integral representations. Further, we discuss the solution of the fractional kinetic equations (FKEs) involving an extended [Formula: see text]-Hurwitz–Lerch [Formula: see text]-function of matrix arguments. In addition, the results investigated in view of an extended [Formula: see text]-Hurwitz–Lerch [Formula: see text]-matrix function are rather general in nature and can easily give various known and novel FKEs.

New results for generalized Hurwitz-Lerch Zeta functions using Laplace transform

“…The extension and generalisation of FKEs involving many fractional operators were found in (Saxena et al [23], Saxena et al [24], Chouhan and Sarwat [25], Chouhan et al [26], Agarwal et al [27], Agarwal et al [28], Agarwal and Nisar [29], Baleanu et al [30], Nisar et al [31], Nisar [32], Şahin and Yagcı [33], Yagcı and Şahin [34], Akel et al [35], and Hidan et al [36]).…”

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

“…On the other hand, recent extensions of special functions build upon the work of esteemed researchers such as Abdalla et al [4,5], Abd-Elmageed et al [6], Hidan et al [7], Fuli He et al [8], and Cuchta et al [9], who have shown a strong interest in studying the extension of special functions in matrix arguments. Contributions to the field by considering various extensions of the gamma, beta, and hypergeometric matrix functions have been documented in [10][11][12][13][14].…”

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].…”