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

Asfand Fahad, Ammara Nosheen, Khuram Ali Khan, Maria Tariq, Rostin Matendo Mabela and Ahmed S.M. Alzaidi

Mathematical and Computer Modelling of Dynamical Systems, 2024, vol. 30, issue 1, 1-15

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 $(\alpha ,s)$(α,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.

Date: 2024
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DOI: 10.1080/13873954.2023.2301075

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