Applications of Ujlayan and Dixit Fractional Uniform Probability Distribution

In this work, we consider the Ujlayan-Dixit (UD) fractional derivative and integral to present the fractional probability density function for the Continuous Uniform Distribution (CUD). Some applications for this distribution using the UD approach are developed by introduce new fractional notions on the probability theory, which involve cumulative distribution, survival and hazard functions. For continuous random variables, various additional concepts and applications are established, including the fractional expectation, the fractional variance and the fractional moments. Finally, the UD fractional standard deviation and the UD fractional Shannon entropy are provided.