A Note on the New Extended Beta Function with Its Application

The purpose of this research is to provide a systematic review of a new type of extended beta function and hypergeometric function using a confluent hypergeometric function, as well as to examine various belongings and formulas of the new type of extended beta function, such as integral representations, derivative formulas, transformation formulas, and summation formulas. In addition, we also investigate extended Riemann-Liouville (R-L) fractional integral operator with associated properties. Furthermore, we develop new beta distribution and present graphically the relation between moment generating function and ℓ.