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GENERALIZED SOLUTIONS OF HAMILTON-JACOBI EQUATIONS WITH FRACTIONAL COINVARIANT DERIVATIVES AND TIME-MEASURABLE HAMILTONIAN
- Authors: Gomoyunov M.I1,2
-
Affiliations:
- N.N. Krassovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
- Ural Federal University
- Issue: Vol 61, No 11 (2025)
- Pages: 1490-1509
- Section: CONTROL THEORY
- URL: https://journals.rcsi.science/0374-0641/article/view/352958
- DOI: https://doi.org/10.7868/S3034503025110054
- ID: 352958
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Abstract
The paper is devoted to the study of generalized in the minimax sense solutions of a Cauchy problem for a (path-dependent) Hamilton-Jacobi equation with fractional coinvariant derivatives under a right-end boundary condition in the case where the Hamiltonian of the equation depends on the time variable in a measurable way. Theorems on the existence and uniqueness of the minimax solution and a theorem on the continuous dependence of this solution on variations of the Hamiltonian and boundary functional are proved. An application of the obtained results to the study of a differential game for a dynamical system described by a differential equation with a Caputo fractional derivative is given.
About the authors
M. I Gomoyunov
N.N. Krassovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS; Ural Federal University
Email: m.i.gomoyunov@gmail.com
Yekaterinburg
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