The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

本文的目的是提出两种求解广义分数阶微分方程的数值技术。我们开发Haar小波运算矩阵，以近似广义Caputo-Katugampola分数阶微分方程的解。此外，我们针对一类广义分数边值问题引入了Green-Haar方法，并将其与经典Haar小波技术进行了比较。在错误分析的上下文中，建立了错误的上限以显示该方法的收敛性。数值实验的结果已以表格和图形格式记录在案，以阐明所提出方法的准确性和效率。进一步，