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Abstract In this study, motivated by the frequent use of Fox-Wright function in the theory of special functions, we first introduced new generalizations of gamma and beta functions with the help of Fox-Wright function. Then by using these functions, we defined generalized Gauss hypergeometric function and generalized confluent hypergeometric function. For all the generalized functions we have defined, we obtained their integral representations, summation formulas, transformation formulas, derivative formulas and difference formulas. Also, we calculated the Mellin transformations of these functions.
Ata et al. (Wed,) studied this question.