A new generalized beta function associated with statistical distribution and fractional kinetic equation

Abstract

Several authors have extensively investigated beta function, hypergeometric function and confluent  hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and science. The main purpose of this paper is to present a new generalization of extended beta function, hypergeometric function and confluent hypergeometric function with the help of m-parameter Mittag-Leffler function, as well as examine some important properties like integral representations, differential formula and summation formulas. We also examine generalized Caputo fractional derivative operator with the help of m-parameter Mittag-Leffler function with associated properties using the generalized beta function. We define a new beta distribution involving the new generalized beta function. The mean, variance, coefficient of variance, moment generating function and characteristic function and cumulative  distribution are derived. Further, we derive the solution of fractional Kinetic equation involving generalized  hypergeometric function.