Hamilton-Jacobi equations involving a Caputo time-fractional derivative
Daniela Di Donato
TL;DR
This paper develops a new representation formula of Hopf-Lax type for subsolutions to Hamilton-Jacobi equations that incorporate Caputo time-fractional derivatives, advancing the mathematical understanding of fractional PDEs.
Contribution
It introduces a novel Hopf-Lax type representation for Hamilton-Jacobi equations with Caputo derivatives, bridging fractional calculus and PDE theory.
Findings
Derived a representation formula for subsolutions
Extended classical Hamilton-Jacobi theory to fractional derivatives
Provides tools for analyzing fractional PDEs
Abstract
We prove a representation formula of intrinsic Hopf-Lax type for subsolutions to Hamilton-Jacobi equations involving a Caputo time-fractional derivative.
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Taxonomy
TopicsFractional Differential Equations Solutions · Nonlinear Differential Equations Analysis · Optimization and Variational Analysis