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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Camilli, Fabio¹  De Maio, Raul¹  Iacomini, Elisa¹ 

[1] Sapienza Univ Roma, Dip Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy

关键词: Caputo derivative;    Riemann-Liouville derivative;    Fractional Hamilton-Jacobi equation;    Hopf-Lax formula;    Subordinator;   

DOI  :  10.1016/j.jmaa.2019.04.069

来源: Elsevier

【 摘 要 】

We prove a representation formula of Hopf-Lax type for solutions to Hamilton-Jacobi equation involving a Caputo time-fractional derivative. Equations of this type are associated with optimal control problems where the controlled dynamics is given by a time-changed stochastic process describing the trajectory of a particle subject to random trapping effects. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free