In this paper, Haar wavelet collocation technique is developed for the solution of Volterra and Volterra–Fredholm fractional integro-differential equations. The Haar technique reduces the given equations to a system of linear algebraic equations. The derived system is then solved by Gauss elimination method. Some numerical examples are taken from literature for checking the validation and convergence of the proposed method. The maximum absolute errors are compared with the exact solution. The maximum absolute and mean square root errors for different number of collocation points are calculated. The results show that Haar method is efficient for solving these equations. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is described in the Caputo sense. All algorithms for the developed method are implemented in MATLAB (R2009b) software.

在本文中，开发了Haar小波配置技术来求解Volterra和Volterra-Fredholm分数阶积分微分方程。Haar技术将给定的方程式简化为线性代数方程式系统。然后通过高斯消除法求解导出的系统。从文献中得到了一些数值示例，以验证所提出方法的有效性和收敛性。将最大绝对误差与精确解进行比较。计算不同数量的搭配点的最大绝对和均方根误差。结果表明，Haar方法对于求解这些方程是有效的。计算出不同数目的搭配点的实验收敛速度，大约等于2。小数导数在Caputo的意义上进行了描述。该开发方法的所有算法均在MATLAB（R2009b）软件中实现。