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Abstract

In this paper, we explore the geometric properties of the Barnes-Mittage-Leffler functions, focusing particularly on their q-close-to-convex behaviors. By examining the relationships between these functions and their geometric constraints, we aim to provide new insights into their applications in complex analysis, geometric function theory, and mathematical physics. Through this exploration, we also highlight potential future directions for further research, especially in the context of fractional calculus and its connection to the geometry of special functions.