Some novel inequalities for Caputo Fabrizio fractional integrals involving (α,s)-convex functions with applications

ABSTRACT

Fractional calculus is extremely important and should not be undervalued due to its critical role in the theory of inequalities. In this article, different generalized Hermite-Hadamard type inequalities for functions whose modulus of first derivatives are $(\alpha ,s)$-convex are presented, via Caputo-Fabrizio integrals. Graphical justifications of main results are presented. Graphs enable us to support our conclusions and show the reliability of our findings. Additionally, some applications to probability theory and numerical integration are also established. As special cases, certain established outcomes from different articles are recaptured. This study acts as a stimulant for future studies, inspiring researchers to investigate more thorough results by utilizing generalized fractional operators and broadening the idea of convexity.

KEYWORDS:

• Convex function
• Caputo-Fabrizio integrals
• power-mean inequality

Acknowledgments

The researchers would like to acknowledge Deanship of Scientific Research, Taif University for funding this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Postdoctoral Fellowship of Asfand Fahad at Zhejiang Normal University, China [YS304023966].