A General Class of Multivariable Mittag–Leffler Function and Its Associated Applications

In this paper, a new class of multivariable special functions and their generalizations is introduced and used to solve generalized fractional differential and kinetic equations. By applying the Sumudu transform, we derive solutions for the fractional differential equations and fractional kinetic equations expressed in terms of Prabhakar’s Mittag–Leffler function and Wiman’s Mittag–Leffler function, respectively. In contrast to previous research, which mostly focused on single‐variable Mittag–Leffler formulations, our method demonstrates the advantage of dealing with multivariable parameters, providing more versatility for modeling complicated fractional systems. With the use of illustrative examples that demonstrate application, this work is innovative in that it unifies and generalizes a number of previously proven results into a unified analytical framework. These results give fractional models, which may find use in physics, engineering, and other applied sciences, a better mathematical basis. MSC2020 Classification 26A33, 33E12, 44A10, 44A05, 44A35