A study of generalized Mittag-Leffler-type function of arbitrary order

Abstract We present a novel generalized Mittag-Leffler-type function of arbitrary order in this study. We look into its fundamental characteristics, such as differential formulas, recurrence relations, integral representations, the Euler, Laplace, Mellin, Whittaker, and Mellin-Barnes transforms. Additionally, we express it using the H-function, generalized hypergeometric function, and Fox-Wright function. Further, for this generalized Mittag-Leffler-type function of arbitrary order, we create fractional integral and differential operators. Also, we derive several intriguing special instances of our fundamental results.