The development of fractional calculus 1695–1900

This paper describes an example of mathematical growth from scholarly curiousity to application. The contributions of Liouville, Riemann, and Laurent to the field of fractional operators are discussed. Motivation for the writing of this paper is based on the statement by Harold T. Davis [1927]: “The great elegance that can be secured by the proper use of fractional operators and the power they have in simplifying the solution of complicated functional equations should more than justify a more general recognition and use.”