A computational algorithm for solving linear fractional differential equations of variable order

Abstract

In this paper, a numerical method for the solution of a class of linear variable-order fractional differential equations (FDEs) is given. For the numerical solution of linear variable order FDEs, we devised the Haar wavelet collocation method (HWCM) with a combination of Caputo fractional derivatives. To illustrate the accuracy of the proposed technique, numerical examples are presented. For checking the efficiency and accuracy of HWCM, some examples are given, also maximum absolute error and mean square root error of each test problem is computed for a different number of collocation points to check the validity and applicability of the proposed method. For various numbers of collocation points, a comparison of exact and approximate solutions is shown in the figure.