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arXiv · 1708.05649

Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives

Wei Liu·Michael Röckner·José Luís da Silva
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Abstract

In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential equations with time-fractional derivatives, including time-fractional (stochastic) porous media equations (including the case where the Laplace operator is also fractional) and $p$-Laplace equations as special cases.

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Wei Liu, Michael Röckner, José Luís da Silva. 2017-08-18. Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives. https://doi.org/10.1137/17m1144593

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