ABSTRACT
The concept of a non-integer differentiation and integration of a function is almost as old as calculus itself. The notion of the one-half derivative of a function was mentioned by G.W. Leibniz in a letter to L'Hospital in 1695[141]. Many famous mathematicians, including Euler, Lagrange, Laplace, Fourier, and Abel, either pondered over the idea or made some contributions to it. But it was not until Liouville and Riemann that the idea became more precisely formulated.
