Methods of Fractional Calculus
摘要
The subject of fractional calculus is believed to have stemmed from de L’Hop̂ital’s question of “What does \(\frac{d^n}{dx^n}f(x)\) mean if \(n=1/2\) ?” to Leibniz, when he shared the notation \(\frac{d^n}{dx^n}f(x)\) to represent the \(n^{th}\) derivative of a function f in the year 1695. Since then, many well-known mathematicians, including Euler, Abel, Liouville and Riemann, have become interested in the fractional calculus and its theory has gradually been extended to incorporate operators \(D^v\) , where v may be rational or irrational, positive or negative, real or complex. Thus, the fractional calculus is the study of differentiation and integration of any arbitrary order. The popular book of [1] on the subject of fractional calculus primarily deals with fractional differentiable equations. The book [2] describes the mathematical arguments which lead to the definitions of types of fractional integrals and fractional derivatives.