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arXiv · 1803.09296

A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time derivative

Fabio Camilli·Raul De Maio·Elisa Iacomini
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Abstract

We prove a representation formula of Hopf-Lax type for the solution of a Hamilton-Jacobi equation involving Caputo time-fractional derivative. Equations of these type are associated with optimal control problems where the controlled dynamics is replaced by a time-changed stochastic process describing the trajectory of a particle subject to random trapping effects.

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Fabio Camilli, Raul De Maio, Elisa Iacomini. 2018-03-25. A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time derivative. https://arxiv.org/abs/1803.09296

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