Certain subclasses of harmonic functions involving $q-$Mittag-Leffler Function

Abstract

In this article, the $q-$ differential operator for harmonic function related with Mittag-Leffler function is described to familiarise a new class of complex-valued harmonic functions which are orientation preserving, univalent in the open unit disc. We conquer certain significant aspects, such as distortion limits, preservation of convolution, and convexity constraints, which are also addressed. Furthermore, with the use of sufficiency criteria, we calculate sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Besides, some of the interesting consequences of our investigation are also included.