In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically.

中文翻译：

---

离散数据的非线性时间分数反应扩散方程的最终值问题

在本文中，我们研究了从最终值数据中找到带有非线性源的多维时间分数反应扩散方程的解的问题。我们证明目前的问题不是很恰当。然后使用截断展开方法（在二维情况下）和拟边界值方法（在多维情况下）构造正则问题。最后，给出了正则解的收敛速度并进行了数值研究。