On Generalized Mittag–Leffler‐Type Functions of Two Variables

ABSTRACT We aim to study the Mittag–Leffler‐type functions of two variables by analogy with the Appell hypergeometric functions of two variables. Moreover, we targeted functions as limiting cases of the functions and studied certain properties, as well. Following Horn's method, we determine all possible cases of the convergence region of the function . Further, for a generalized hypergeometric function, (two‐variable Mittag–Leffler‐type function) integral representations of the Euler type have been proved. One‐dimensional and two‐dimensional Laplace transforms of the function are also defined. We have constructed a system of partial differential equations which is linked with the function .

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