The study reveals properties of the mittag-leffler function in terms of differential formulas and transforms, highlighting its applications.
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.
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Bin-Saad et al. (2025) studied this question.
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