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

2018/03/25 by Fabio Camilli, Camilli, Fabio, Raul De Maio +3
Mathematics · Physics and Astronomy · #26A33 #35R11 #49L20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1803.09296

openalex publication_date 2018/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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