Abstract
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.
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Ouedjedi, Y., Rougirel, A. & Benmeriem, K. Galerkin method for time fractional semilinear equations. Fract Calc Appl Anal 24, 755–774 (2021). https://doi.org/10.1515/fca-2021-0033
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DOI: https://doi.org/10.1515/fca-2021-0033