Herein, we consider an effective numerical scheme for numerical evaluation of three classes of space-time-fractional partial differential equations (FPDEs). We are going to solve these problems via composite collocation method. The procedure is based upon the bivariate Müntz–Legendre wavelets (MLWs). The bivariate Müntz–Legendre wavelets are constructed for first time. The bivariate MLWs operational matrix of fractional-order integral is constructed. The proposed scheme transforms FPDEs to the solution of a system of algebraic equations which these systems will be solved using the Newton’s iterative scheme. Also, the error analysis of the suggested procedure is determined. To test the applicability and validity of our technique, we have solved three classes of FPDEs.

中文翻译：

---

求解时空分式偏微分方程的二元Müntz小波复合配置方法

在这里，我们考虑一种有效的数值方案，用于对三类时空分形偏微分方程（FPDE）进行数值评估。我们将通过复合搭配方法解决这些问题。该程序基于二元Müntz-Legendre小波（MLW）。二元Müntz-Legendre小波是第一次构造。构造分数阶积分的二元MLWs运算矩阵。拟议的方案将FPDE转换为代数方程组的解，这些系统将使用牛顿迭代方案进行求解。同样，确定建议程序的错误分析。为了测试我们技术的适用性和有效性，我们解决了三类FPDE。