$\psi$-Hilfer-Atangana-Baleanu Fractional Integral Operators and some Fractional Integral Inequalities
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Authors: S. KERMAUSUOR, D. DENU AND P. O. OLANIPEKUN
DOI: 10.46793/KgJMat2610.1585K
Abstract:
We present new fractional integral operators known as the left- and right-sided ψ-Hilfer-Atangana-Baleanu fractional integral operators. These fractional integrals generalize the Atangana-Baleanu and the ABK fractional integral operators. As a practical application, we derive a generalization of the Hermite-Hadamard inequality for s-convex functions in the second sense, utilizing the newly defined integral operators. Additionally, we established several Hermite-Hadamard type fractional integral inequalities for functions whose derivatives in absolute value raised to some nonnegative powers are s-convex in the second sense, using the ψ-Hilfer-Atangana-Baleanu fractional integral operator. We also present some specific cases of our main results.
Keywords:
Hermite-Hadamard inequality, Atangana-Baleanu fractional integral operators, fractional integral inequalities, convex functions, Hölder’s inequality, power mean inequality, s-convex functions.
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