On Applications of Fractional Calculus Involving Summations of Series

A significantly large number of earlier works on the subject of fractional calculus give interesting account 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 obtain number of summations of series concerning generalized hypergeometric functions. Our finding provides interesting unifications and extensions of a number of new and known results.