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October 27, 2025Open Access

k-Fractional Extension of h-Hadamard Integrals and Derivatives

Key Points

New properties of k-fractional h-Hadamard integrals were defined, indicating a significant advancement in integral analysis.
Important propositions have been introduced, enhancing the understanding of k-fractional operators.
The study utilizes theoretical frameworks to explore these generalized derivatives and integrals in mathematical analysis.
This work suggests that extending these theories may lead to further advancements in fractional calculus.

Abstract

In this paper, we present a generalization types of the h-Hadamard integrals and derivatives parameterized by k. The h-Hadamard integrals and derivatives are themselves generalizations of the Hadamard integrals and derivatives, defined in relation to a continuous function h. We have also developed the concepts of k-gamma and k-beta, which correlate with the definitions of k-fractional h-Hadamard integrals and derivatives. The paper includes various theorems, propositions, properties, and illustrative examples

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