Unification and extension of classical integral theorems via the generalized Mittag–Leffler function

This paper presents theorems on Euler's Beta type integrals in both single and double forms that include the generalized Mittag–Leffler (ML) function. ML function that used here is of arbitrary order with six parameters in a given different arguments performed in the Euler's Beta type integrals. Numerous special cases are derived and given as many corollaries demonstrate integrals involving ML, Fox-Wright (F-W) and Hypergeometric functions. The obtained results are given directly in terms of the hypergeometric, F-W and ML functions. The present study covers and generalizes many previous results and theories at a certain given parameters. This study is considered a fundamental core for many future applications directly using the proven results.