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.
A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative / Camilli, Fabio; De Maio, Raul; Iacomini, Elisa. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 477:2(2019), pp. 1019-1032. [10.1016/j.jmaa.2019.04.069]
A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative
Camilli, Fabio
;De Maio, Raul;IACOMINI, ELISA
2019
Abstract
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.| File | Dimensione | Formato | |
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