Certain Properties of Generalized Mittag‐Leffler Function and Their Application

ABSTRACT The paper explores the derivation of novel recurrence relations for two parametric Mittag‐Leffler (M‐L) functions and investigates their intriguing applications. Additionally, the study establishes valuable and captivating connections between one parametric and two parametric M‐L functions through the derived recurrence relations. Furthermore, the paper presents intriguing expressions for several elementary functions in relation to the two parametric M‐L function and reciprocally expresses M‐L functions in terms of elementary functions. Leveraging the recurrence relations, the study also establishes relationships among Fox–Wright functions using Saigo and Riemann–Liouville fractional calculus operators and extends these relationships to their specific instances. The paper sets forth various research challenges for future investigations in this domain.