Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators

Abstract

This study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for differentiable convex functions. In the findings section, firstly, an integral identity is obtained and various integral inequalities are obtained based on this identity. The peculiarity of the results is that a hybrid operator has been used in inequality theory, which includes the derivative and integral operators together.

Keywords

• Hadamard type inequalities
• Caputo derivative
• the proportional Caputo-hybrid operator