Most of fractional differential Equations are considered on a fixed Interval. In this paper, we consider a typical fractional differential Equation on a symmetric Interval $[-\alpha,\alpha]$, where $\alpha$ is the order of fractional derivative. For a positive real number α we prove that the solutions are  $T_{n,\alpha}(x)=(\alpha+x)^\frac{1}{2}Q_{n,\alpha}(x)$ where $Q_{n,\alpha}(x)$ produce a family of orthogonal polynomials with respect to the weight function$w_\alpha(x)=(\frac{\alpha+x}{\alpha-x})^{\frac{1}{2}}$ on $[-\alpha,\alpha]$. For integer case $\alpha = 1 $, we show that these polynomials coincide with classical Chebyshev polynomials of the third kind. Orthogonal properties of the solutions lead to practical results in determining solutions of some fractional differential Equations.

In this paper, the Block pulse functions (BPFs) and their operational matrices of integration and differentiation are used to solve Lienard Equation in a large Interval. This method converts the Equation to a System of nonlinear algebraic Equations whose solution is the coefficients of Block pulse expansion of the solution of the Lienard Equation. Moreover, this method is examined by comparing the results with the results obtained by the Adomian decomposition method (ADM) and the Variational iteration method (VIM).

In this paper, Interval Legendre wavelet method is investigated to approximated the solution of the Interval Volterra-Fredholm-Hammerstein integral Equation. The shifted Interval Legendre polynomials are introduced and based on Interval Legendre wavelet method is de ned. The existence and uniqueness theorem for the Interval Volterra-Fredholm-Hammerstein integral Equations is proved. Some examples show the e ectiveness and e ciency of the approach.