In order to solve the nonlinear time fractional inverse parabolic equations, two methods namely, combination of the finite difference method (FDM) and cubic B-spline collocation method are proposed. By using a sensor placed at a point inside the body and measuring the temperature at $x=x^{\ast }$, $0<x^{\ast }<1$, and applying the FDM to the inverse problem, a stable numerical solution to this problem is determined. Comparison of the approximate solution with the exact one shows that the used approach is simple and practical.

中文翻译：

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时间分数逆抛物线问题的混合格式

为了求解非线性时间分数阶逆抛物线方程组，提出了有限差分法（FDM）和三次B样条配点法相结合的两种方法。通过使用放置在体内某个点的传感器并在$X=X^{\ast }$， $0<X^{\ast }<\mathrm{1个}$，并将FDM应用于反问题，即可确定该问题的稳定数值解。将近似解与精确解进行比较表明，所使用的方法简单实用。