Application of Ujlayan-Dixit Fractional Exponential Probability Distribution

This research aims to present the probability density functions of random variables for exponential distribution by applying a new technique of the Ujlayan-Dixit (UD) fractional derivative and to find some basic concepts related to probability distributions of random variables, which is density, cumulative distribution, survival and hazard functions. In addition, we provides the UD fractional isotopes with the expected values, rth-moments, rth-central moments, mean, variance, skewness and kurtosis. Finally, we give the UD fractional analogs to some entropies measures such as Shannon, Renyi, and Tsallis entropy.