This work addresses a hybrid scheme for the numerical solutions of time fractional Tricomi and Keldysh type equations. In proposed methodology, Haar wavelets are used for discretization in space while \(\theta\)-weighted scheme coupled with second order finite differences and quadrature rule are employed for temporal discretization and fractional derivative respectively. Stability of the proposed scheme is described theoretically and validated computationally which is an essential chunk of the current work. Efficiency of the suggested scheme is endorsed through resolutions level and time step size. Goodness of the obtained solutions confirmed through computing error norms \({\mathbb E}_{\infty }\), \({\mathbb E}_2\) and matching with existing results in literature. Moreover, convergence rate is also checked for considered problems. Numerical simulations show good performance for both 1D and 2D test problems.

这项工作解决了时间分数Tricomi和Keldysh型方程数值解的混合方案。在所提出的方法中，将Haar小波用于空间离散化，而将\（\ theta）加权方案与二阶有限差分和正交规则结合起来分别用于时间离散化和分数阶导数。从理论上描述了所提出方案的稳定性，并在计算上进行了验证，这是当前工作的重要组成部分。所建议方案的效率通过分辨率级别和时间步长得到认可。通过计算错误准则\（{\ mathbb E} _ {\ infty} \），\（{\ mathbb E} _2 \）所确认的解决方案的优劣并与文献中的现有结果相匹配。此外，还检查了收敛速度以查找所考虑的问题。数值模拟显示了针对1D和2D测试问题的良好性能。