Competent Condition For Geometric Properties Q-Starlikeness And Q-Convexity Of Mittag-Leffler Function

  • Deepa Amit Karwa
  • Seema Kabra
Keywords: Univalent function, q-derivative operator, q-starlike function, q-convex function, Mittag Leffler function.

Abstract

This paper focus on the competent conditions for q-starlikeness and q-convexity of the Mittag-Leffler function. The Mittag-Leffler function, a generalization of the exponential function, plays a critical role in fractional calculus and differential equations. This work examines the function within the framework of q-calculus, an extension of classical calculus that introduces a deformation parameter q.

We derive sufficient conditions under which the Mittag-Leffler function exhibits q-starlikeness and q-convexity, properties that are pivotal for ensuring the function's regularity and univalence in specific domains. Utilizing techniques from geometric function theory, we establish criteria that involve the parameters of the Mittag-Leffler function and the deformation parameter q. Our results are found in terms of Fox Wright function which  provide a comprehensive understanding of how these parameters influence the geometric behavior of the function, thereby contributing to the broader theory of q-analytic functions. This investigation not only extends the existing theory of the Mittag-Leffler function but also opens new pathways for its application in mathematical and physical problems characterized by q-deformations.

Author Biographies

Deepa Amit Karwa

Department of Mathematics, Sangam University, Bhilwara, Raj., INDIA. 

Seema Kabra

Sharad Institute of technology college of Engineering, Yadrav, Maharashtra, INDIA

 

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Published
2024-08-25
How to Cite
Deepa Amit Karwa, & Seema Kabra. (2024). Competent Condition For Geometric Properties Q-Starlikeness And Q-Convexity Of Mittag-Leffler Function. Revista Electronica De Veterinaria, 25(1), 935-941. https://doi.org/10.69980/redvet.v25i1.753
Section
Articles