This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. This method has the advantage of not being more complicated than the one used to solve the same PDE with first order time derivative. As a model problem, existence and uniqueness is proved for semilinear heat equations with polynomial growth at infinity.

中文翻译：

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时间分数半线性方程的伽辽金方法

本文收集了使用 Galerkin 方法求解 Riemann-Liouville 时间分数非线性偏微分方程的工具。这种方法的优点是不比用于求解具有一阶时间导数的相同 PDE 的方法复杂。作为一个模型问题，证明了多项式在无穷远处增长的半线性热方程的存在唯一性。