In this paper, the time fractional reaction-diffusion equations with the Caputo fractional derivative are solved by using the classical $L1$-formula and the finite volume element (FVE) methods on triangular grids. The existence and uniqueness for the fully discrete FVE scheme are given. The stability result and optimal \textit{a priori} error estimate in $L^2(\Omega)$-norm are derived, but it is difficult to obtain the corresponding results in $H^1(\Omega)$-norm, so another analysis technique is introduced and used to achieve our goal. Finally, two numerical examples in different spatial dimensions are given to verify the feasibility and effectiveness.

翻译：在本文中,与Caputo分数衍生物的时分反扩散方程式在三角网格上采用经典的1美元公式和有限体积元素(FVE)方法来解决。给出了完全独立的FVE方案的存在和独特性。得出了稳定结果和最佳的L2(\Omega)美元-Norm误差估计值,但很难获得以$H1(\Omega)美元-norm得出的相应结果,因此引入了另一种分析技术,用于实现我们的目标。最后,给出了两个不同空间层面的数字实例,以核实可行性和有效性。