Analysis of Fractional Systems using Haar Wavelet

Abstract

Wavelets are relatively new tool and have quite been thriving domain in mathematical research. Numerical solutions of differential and integral equations require development of accurate and fast algorithms based on wavelets. This is more pertinent for those problems having localized solutions, both in position and scale. Haar wavelet offers a promising solution bases due to simple mathematical expressions and multi-resolution properties. In this paper, A Haar wavelet based method to solve partial differential equations (PDE) modeling fractional systems is presented. Operational approach is based on representing various integro-differential mathematical operations in terms of matrices. In this article, firstly introduction of Haar wavelet and different operational matrices used for the analysis of fractional systems are presented. A modified computational technique is explained to solve variety of partial differential equations modeling systems of fractional order. This method achieves the solutions by solving Sylvester equation using MATLAB. Demonstrations are provided with the help of two illustrative examples by suitable comparisons with exact solutions.