Abstract:

In order to solve the Fredholm integro-differential equations of fractional order with variable coefficient, By using Caputo fractional derivative and property, the arbitrary order derivatives expressed by Legendre polynomial are acquired, then using Legendre series on the approximation in the interval, the fractional integral differential equations can be changed into matrix form of the equation, using collocation method. The original integral differential equations numerical solution are obtained. A numerical example is presented, which verifying the feasibility and effectiveness of the method.

Key words: Legendre polynomial; fractional calculus; variable coefficient; Caputo derivative; numerical solution