Numerical solution of fractional differential equation by wavelets and hybrid functions

Abstract

In this paper, we introduce methods based on operational matrix of fractional order integration for solving a typical n-term non-homogeneous fractional differential equation (FDE). We use Block pulse wavelets matrix of fractional order integration where a fractional derivative is defined in the Caputo sense. Also we consider Hybrid of Block-pulse functions and shifted Legendre polynomials to approximate functions. By uses these methods we translate an FDE to an algebraic linear equations which can be solve. Methods has been tested by some numerical examples.