Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Fractional differential equations with Legendre polynomials

Solving the fractional integro-differential equations using fractional order Jacobi polynomials

In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra  integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, the...

Numerical solutions of fractional Riccati type differential equations by means of the Bernstein polynomials

In this paper, a collocation method based on the Bernstein polynomials is presented for the fractional Riccati type differential equations. By writing t? ta (0 < a < 1) in the truncated Bernstein series, the truncated fractional Bernstein series is obtained and then it is transformed into the matrix form. By using Caputo fractional derivative, the matrix forms of the fractional derivatives are ...

Solving multi-order fractional differential equations by reproducing kernel Hilbert space method

In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...

numerical solution of multi-order fractional differential equations via the sinc collocation method

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...