The Hadamard-type inequalities for modified exponential trigonometric convex functions and Chebyshev-type inequalities obtained via a fractional integral operator

This thesis presents a comprehensive survey of fractional integral operators and Chebyshev-type integral inequalities. The thesis consists of five main chapters, each chapter focusing on a specific topic and aiming to provide the reader with an in-depth understanding. The first chapter deals with the historical development and importance of inequalities, fractional analyses, fractional differentiation and integration, as well as fractional integral operators. This chapter provides the historical background of the subject and the evolution of mathematical thought, thus arousing the reader's interest. The second chapter contains the basic definitions and theorems related to fractional analysis and integral operators and helps the reader to grasp the fundamentals of the subject. This chapter provides a solid mathematical framework of fractional integrals. In the third chapter, the definitions and properties of various fractional integral operators in the litterateur are analysed. This chapter aims to extend the application areas of fractional integral operators by contributing to the existing knowledge. The fourth chapter presents some new inequalities and integral operators obtained with the newly defined class of convex functions and Chebyshev type integral inequalities. This section presents important findings from both theoretical and practical points of view. In the fifth chapter, the results obtained and suggestions for future work are presented. This chapter provides an overall evaluation of the research and suggests new directions for the development of the field. The thesis aims to make significant contributions to the field of fractional analysis and brings new perspectives to the related litterateur.