Some Miscellaneous Properties and Applications of Certain Operators of Fractional Calculus

Abstract

In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields. The main object of this paper is to consider some miscellaneous properties and applications which are associated with several fractional differintegral operators. We first investigate, in a systematic and unified manner, various families of series identities which emerged in connection with some of these fractional differintegral formulas. By using such operators of fractional calculus, a number of integral formulas as well as fractional differintegral formulas involving inverse hyperbolic functions are also evaluate.