In this paper, we investigate some new inequalities based on the Riesz-type fractional integral operator for synchronous and bounded functions.

In this paper, we investigate some Tur\’{an}-type inequalities for the hypergeometric superhyperbolic sine and cosine functions associated with Kummer confluent hypergeometric series of first type.

This paper is devoted to the study of Tur\’{an} type inequalities for some well-known special functions such as supersine and supercosine which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality.