Some operators of fractional calculus and their applications regarding various complex functions analytic in certain domains

In this academic research note, some familiar operators prearranged by fractional-order calculus will first be introduced and various characteristic properties of those operators will next be propounded. Through the instrumentality of various earlier results associating with both those operators and some complex- exponential forms, and also in the light of certain special information in [1], [20], [17] and [38], an extensive result together with a variety of its implications consisting of several exponential type inequalities will then be determined. A number of its possible implications will extra be pointed out. Mathematics Subject Classification (2010): 26A33, 30A10, 34A40, 35A30, 41A58, 30C45, 30C55, 30C80, 33D15, 26E05, 33E20.