@article{Aljawi2026, 
author = {Salma Aljawi and Vinod Kumar Jatav and Ankit Pal},
title = {On the five-parameter Mittag-Leffler matrix function and its properties},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17382-17398},
keywords = {Mittag-Leffler functions, matrix functional calculus, generalized fractional calculus},
url = {https://www.sciopen.com/article/10.3934/math.2026711},
doi = {10.3934/math.2026711},
abstract = {In this paper, we introduce and study a matrix analog of the five-parameter Mittag-Leffler function. We establish the absolute convergence of the series defining this function on the unit circle        |    ϖ      |    =  1 under certain spectral conditions. Several fundamental properties are derived, including integral representations, derivative formulas, and differential recurrence relations. Furthermore, we obtain a variety of finite summation formulas for this matrix function and its related Fox-Wright matrix analog. Finally, we investigate the composition of the function with generalized fractional calculus operators introduced by Katugampola, deriving closed-form expressions for both fractional integrals and derivatives. The results presented here extend the theory of special matrix functions and contribute to the field of fractional calculus.}
}