New integral inequalities with variable order Riemann-Liouville fractional integral operators for differentiable convex functions of different kinds

In this thesis, new variable-order Hermite-Hadamard type integral inequalities have been obtained for different types of differentiable convex functions by using the Riemann-Liouville fractional integral operator. In the first section, the introduction, a brief overview of the history of convex functions and inequality theory is provided, along with information on related works in the literature. In the second section, the theoretical foundations, basic definitions, and concepts related to convex functions, as well as some classes of differentiable convex functions, are discussed. The third section, Material and Methods, presents a detailed literature review on the integral inequalities that will be used. In the fourth section, following the basic proof methods of mathematical analysis and using the Riemann-Liouville fractional integral operator, some new definitions and theorems for variable-order Hermite-Hadamard type integral inequalities are derived with the help of fundamental concepts of functional analysis.