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Minimax Theory and its Applications 05 (2020), No. 2, 199--220
Copyright Heldermann Verlag 2020

Approximation of Hamilton-Jacobi Equations with the Caputo Time-Fractional Derivative

Fabio Camilli
Dip. di Scienze di Base e Applicate per l'Ingegneria, UniversitÓ di Roma "La Sapienza", 00161 Roma, Italy

Serikbolsyn Duisembay
King Abdullah University of Science and Technology, CEMSE Division, Thuwal 23955-6900, Saudi Arabia

We investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for the approximation of the Hamiltonian. We show that the approximation scheme so obtained is stable under an appropriate condition on the discretization parameters and converges to the unique viscosity solution of the Hamilton-Jacobi equation.

Keywords: Fractional Hamilton-Jacobi equation, Caputo time derivative, finite difference, convergence.

MSC: 35R11, 65L12, 49L25.

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