Fractional Calculus Origin And Evolution Of The Concept

The fractional calculus was proposed bases on the comparison with the classical calculus. The development of the fractional calculus and classical calculus is closely connected. The application of fractional calculus is an international research topic, because of that the fractional calculus has widespread applications. The paper mainly studies on the origin of the concept of the fractional calculus, as well as two definitions of fractional differential and integral.In this paper, the main body of content roughly divided into the following several aspects:Firstly, the meaning of a derivative of integer order (?) can be extended to have meaning if n is an arbitrary number. To solve the problem, mathematicians and scholars had tried to integer derivative theory as the starting point and then extended to arbitrary order derivative. It is showed from the existing literature that the test of mathematicians and scholars is necessary, although it has no substantial achievements.Secondly, It is experienced a long process from the posing to establishment of the concept of the fractional calculus. This section primarily explores the researches of mathematicians. Further, it also clears the origin of the first definition of the fractional calculus. And then, the section indicates the solid foundation which brings from the definition of the fractional calculus.Thirdly, the paper mainly focuses on the research of Grunwald-Letnikov fractional calculus definition and Riemanna-Liouville fractional calculus definition and relationship.