New Version of Simpson Type Inequality for Ψ-Hilfer Fractional Integrals
DOI:
https://doi.org/10.62298/advmath.3Keywords:
Simpson's Type Inequality, Integral Inequalities, Bounded FunctionsAbstract
The ψ-Hilfer fractional integrals serve as a generalization encompassing well-known fractional integrals like Riemann-Liouville and Hadamard fractional integrals. This investigation initiates by demonstrating a key identity tied to ψ-Hilfer fractional integrals, specifically tailored for differentiable functions. Leveraging this identity, we establish a series of Simpson-type inequalities applicable to ψ-Hilfer fractional integrals. To achieve this, we delve into the realms of convexity and the renowned Hölder inequality. Furthermore, we explore the correlations between our primary discoveries and preceding research endeavors.
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