Some applications of fractional calculus involving summation of infinite series

摘要

A significantly large number of earlier works on the subject of fractional calculus give interesting accounts of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to examine rather systematically (and extensively) some of the most recent contributions on the applications of fractional calculus operators in finding the sums of an interesting family of infinite series. Various further generalizations, relevant to the present investigation, are also given.