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

TL;DR

This paper introduces a method for solving evolution equations with time-fractional derivatives on Gelfand triples, applicable to both deterministic and stochastic quasi-linear PDEs, including fractional porous media and p-Laplace equations.

Contribution

It develops a novel approach based on monotonicity techniques for time-fractional evolution equations, extending to stochastic cases and fractional operators.

Findings

Method successfully solves time-fractional (stochastic) PDEs

Applicable to fractional porous media and p-Laplace equations

Extends existing techniques to new classes of equations

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.