Some new Chebyshev and Grüss-type fractional inequalities obtained by a generalized fractional integral operator

In this thesis, a generalized fractional integral operator, which generalizes some fractional integral operators existing in the literature, is addressed. The thesis consists of five main sections. In the first section, the historical development and importance of topics such as inequalities, fractional analysis, fractional derivatives and integrals, and fractional integral operators are emphasized. The second section provides fundamental definitions and theorems related to these topics. The third section presents definitions of some existing fractional integral operators and generalized fractional integral operators found in the literature. In the fourth section, some new inequalities obtained with the generalized fractional integral operator are presented. Finally, the fifth section includes conclusions and recommendations.