(untitled) (Journal of Advances and Scholarly Researches in Allied Education, 2024)
Mittag-Leffler functions, introduced by Gösta Mittag-Leffler in 1903, play a pivotal role in fractional calculus and numerous applied sciences. They generalize exponential functions and are characterized by their rich structure, which enables modeling of processes exhibiting memory and hereditary properties. The Mittag-Leffler function emerges as a natural solution to fractional differential equations, making it invaluable in areas such as viscoelasticity, anomalous diffusion, and control theory. Recent advancements have extended its applications to stochastic processes, bioengineering, and mathematical physics. This paper explores the fundamental properties, analytical behavior, and diverse applications of Mittag-Leffler functions, highlighting their importance in solving complex real-world problems.