“YANGI AVLOD ILMIY TADQIQOTLARI” respublika ilmiy-amaliy konferensiyasi
CONVERGENCE OF A NEW TRIVARIATE MITTAG-LEFFLER-TYPE FUNCTION
Fergana State University
This paper introduces a new trivariate Mittag-Leffler type function and investigates its fundamental properties. The regions of convergence of the triple power series are established, an integral representation is derived, and corresponding estimates are obtained. The convergence analysis is carried out using Horn's method, supported by the asymptotic behavior of the gamma function for large arguments. Six distinct cases are examined depending on various combinations of the parameters, and in each case the conditions for absolute convergence of the series are determined. The results obtained are relevant to the theory of fractional differential equations, particularly for problems involving the Prabhakar fractional derivative.