FRACTIONAL CALCULUS OPERATORS AND THEIR APPLICATIONS INVOLVING POWER FUNCTIONS AND SUMMATION OF SERIES

Many earlier works on the subject of fractional calculus contain inter esting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis (such as ordin ary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to examine rather s ystematically (and extensively some of the most recent;contributions o n the applications of fractional calculus operators involving power fu nctions and in finding the sums of several interesting families of inf inite series. Various other classes of infinite sums found in the math ematical Literature by these (or other) means, and their validity or h itherto unnoticed connections with some known results, are also consid ered. (C) Elsevier Science Inc., 1997