On Some Measures, Analogues to Carlson’s dirichlet Measure, Average, Generlize Erde’lyi-Kober Integral Operators and Applications

Abstract

In the present paper, we define two measures identical to Carlson’s Dirichlet measure and then, with them, find two integral averages and again, construct two generalized fractional integral operators involving these averages those are analogues to generalized Erde’lyi-Kober integral operators. Then, we make their applications to evaluate the transformation formulae of elementary functions on analytic continuation theory. Also, we discuss some of their particular cases