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Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities
(Springer, 2022) Nazeer, Nazakat; Asjad, Muhammad Imran; Azam, Muhammad Khursheed; Akgül, Ali
In this work, we use generalized form of Caputo-type fractional derivative and Riemann–Liouville fractional Integral which is known as Katugampola fractional derivative. This work deals with some results having applications of Katugampola fractional derivative. We discuss commutative and inverse property of Katugampola fractional derivative. We have also introduced Chebyshev inequalities and some other integrals inequalities applying the Katugampola fractional derivative. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Study of the results of Hilbert transformation for some fractional derivatives
(Taylor & Francis Inc, 2024) Nazeer, Nazakat; Akgul, Ali; Ali, Faeem
Caputo Fractional Derivative is a base for the Riemann-Liouville Derivative, Katugampola fractional derivative, and other fractional derivatives. In this paper, we have illustrated several critical features of the Caputo Derivative via Hilbert Transformation that have not yet been discussed. We have also investigated the behavior of the Riemann-Liouville integral and studied the results of the k-Riemann-Liouville fractional integral with the applications of Hilbert transformation.