A fractional-order Legendre function method for numerical solution of fractional differential equations

In this paper, numerical solutions of the multi-order linear fractional differential equations with initial conditions where fractional derivatives are considered in the Caputo sense, have been obtained by fractional-order Legendre function (FLF) method. The fractional-order generalized Taylor functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration for FLFs. The mentioned equations are transformed into a system of algebraic equations. Finally, a numerical example is shown to illustrate the efficiency of the approach.