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This paper investigates certain new weighted Young- and Pólya–Szegö-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. A large quantity of usable classical inequalities in the literature are included in the main results of this paper. Meanwhile, two types of new generalized weighted fractional integral operators are introduced to establish some new weighted Young- and Pólya–Szegö-type inequalities. As applications, several estimates of Chebyshev-type weighted unified fractional integral inequalities with two unknown functions are obtained by employing the Heaviside unit step function. Finally, some relations between main results and known inequalities for different kinds of fractional integral operators are provided.
Wengui Yang (Wed,) studied this question.
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