k-Fractional Extension of h-Hadamard Integrals and Derivatives - Talib Khathem, Sajad; Hamza Geem, Methaq (Journal of Al-Qadisiyah for Computer Science and Mathematics, 2025)
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