Fractional Calculus

Abstract

Fractional calculus is the study of traditional calculus with operations of integration and differentiation of fractional order. The origin of this study came from the question from L’Hospital to Leibniz in 1695 about the meaning of the half-order derivative of functions. This question becomes the first study of fractional calculus and consequently attracted the interest of many well-known mathematicians such as Euler, Liouville, Laplace and Riemann.
This paper presents the brief history of fractional derivatives, the widely used definitions, the new definition and the applications in other fields, for examples, rheology, viscoelasticity and the immune effectors of cancer cells model.