A Numerical Method for Linear Fractional Differential Equations
Fractional order differential equations(FDEs) have received considerable attention in various engineering and applied mathematics fields because of their ability to model complex problems. In most of those problems, FDEs do not have any analytical solutions. Therefore there is a considerable effort to develop numerical methods for the solution of the FDEs. Some of those methods involve various wavelets. In this study, we develop a numerical method for linear FDEs using the Hermite wavelets. Hermite wavelets are orthogonal, which provides sparser operational matrices for fractional orders, which in turn reduces the required computational load.The Hermite wavelet operational matrix is obtained to reduce the FDEs to a system of algebraic equations in the proposed method. The method is simulated throughout illustrative examples and the results are presented.
Keywords – Hermite Wavelets, Linear Fractional Order Differential Equations, Hermite Wavelet Operational Matrix, Block Pulse Functions