The Properties Of Fractional Calculus And Their Applications

Compared with integer calculus,fractional calculus can be more concise and accurate in describing complex mechanical and physical processes,such as historical memory and spatial global correlation.Thereinto,the application of Caputo fractional calculus in physics,mechanics and other fields has been paid more and more attention.In this paper,Caputo fractional calculus and fractional derivative and calculus are introduced briefly.And several related important properties are proved by reasoning.Finally,the application of variable substitution in Caputo fractional calculus is presented and discussed.This paper also summarizes some specific application of variable substitution method in fractional calculus in the synthesis,properties by using variable substitution method that left Riemann-Liouville fractional integral operator,solving the problem of right Riemann-Liouville fractional integral,calculation of G-L type fractional derivative and Caputo fractional derivative,and application in Caputo and Riemann-Liouville fractional differential equations.The aim of this paper is to provide a more detailed theoretical basis for the application of Caputo fractional calculus in physics and mechanics.