On Caputo <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Derivatives and Associated Inequalities

Abstract

This paper studies the k-fractional analogue of the Caputo fractional derivatives, their properties, and applications. A convolution of two functions instead of the product is analyzed by means of Caputo k-fractional derivatives. By virtue of defined convolution Chebyshev type, inequalities have been investigated. Moreover, Hadamard Caputo fractional inequalities have been estimated by using definition of quasi-convex functions.

Keywords

• Caputo fractional derivative
• Chebyshev inequality
• quasi-convex function
• Hadamard inequality