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.
Keywords: Chebyshev inequalities; Katugampola fractional derivative; Mellin transformation; Synchronous function.
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