Visualizing fractional inequalities through 2D and 3D graphs with applications

Abstract

In this paper, we establish a novel identity by leveraging fractional integral operators of Riemann-type. Subsequently, we employ this identity to investigate Bullen's fractional integral inequalities within the framework of classical convex functions. The validity of these innovative inequalities is verified through the visualization of 2D and 3D graphs. Furthermore, we obtain certain well-known results as special cases to our main findings and express them as remarks. Lastly, we derive differences in mean estimates, which serve as valuable tools for representing complex information, facilitating decision-making and aiding analysis in various fields.

Keywords

• Bullen's-type inequalities
• Estimates of mean differences
• Hölder's inequality
• Generalized fractional integrals