Application of Ujlayan-Dixit fractional chi-square probability distribution

In this study, we take into account the Ujlayan-Dixit (UD) fractional derivative in order to introduce the fractional probability density function for the Chi-Square distribution (CSD), and to establish certain new applications for this distribution through the use of fractional concepts in probability theory, such as cumulative distribution, survival and hazard functions. Furthermore, other ideas and applications for continuous random variables are developed using the UD fractional analogs of statistical measures wiche is expectation, r_th-moments, r_th-central moments, variance and standard deviation. Lastly, we provide the UD fractional entropy measures including Shannon, Tsallis and Rényi entropy.