A New Wavelet Operational Method Using Block Pulse and Haar Functions for Numerical Solution of a Fractional Partial Differential Equation

The fractional calculus has many applications in applied science and engineering. The solution of the differential equation containing fractional derivative is much involved. An effective and easy-to-use method for solving such equations is needed. However not only the analytical solutions exist for a limited number of cases, but also the numerical methods are very complicated and difficult. In this paper, a wavelet operational method has been applied based on the operational matrices of the orthogonal functions. By using the operational matrix of integration, a linear fractional partial differential equation has been solved numerically. In the present paper, the Haar wavelet has been used and then from matrix equation, we obtain the algebraic equations suitable for computer programming. The simplicity, clarity and powerfulness of the method has been cited through an illustration.