We investigate numerical solutions of fractional-order Tricomi equation (LFTE) in fractal transonic flow media by employing the method of local fractional q-homotopy transform (LFq-HATM). This method is a combination of methods of homotopy analysis and q-Laplace transform. We express the solutions in terms of rapidly convergent power series where the basics functions are easily computable by Mathematica software. We present uniqueness and convergence analysis of the model via Banach‘s fixed point theory (BFPT). Reliability analysis of the numerical method is provided by figures and physical works. Obtained results indicate the strength and efficiency of the LEq-HATM.

我们采用局部分数q-同伦变换（LFq-HATM）的方法研究分数阶跨音速流动介质中分数阶Tricomi方程（LFTE）的数值解。该方法是同态分析和q-Laplace变换方法的组合。我们以快速收敛的幂级数表示解决方案，在该系列中，基本功能可以通过Mathematica软件轻松计算。我们通过Banach的不动点理论（BFPT）介绍了该模型的唯一性和收敛性分析。数值方法的可靠性分析由图形和物理工作提供。获得的结果表明LEq-HATM的强度和效率。