Simpson-type inequalities for generalized riemann-liouville fractional integrals

This thesis examines Simpson-type inequalities using right-hand and left-hand Riemann-Liouville fractional integrals via the generalized fractional integral operator. Comprising five chapters, the first chapter serves as an introduction. The second chapter covers fundamental concepts, definitions, and theorems needed in subsequent chapters. Chapters three and four address Simpson-type inequalities for single-variable and two-variable functions, respectively. In these chapters, various equations are proven using right-hand and left-hand Riemann-Liouville fractional integrals via the generalized fractional integral operator. Simpson-type inequalities for differentiable convex functions and convex functions in coordinates are obtained using generalized fractional integrals. Furthermore, different Simpson-type inequalities are formulated using the well-known Hölder and power-average inequalities. Finally, some special cases that can be derived from the main results are presented.