On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order

• Autorzy: Majewski Marek

Identyfikatory

DOI

10.7494/OpMath.2023.43.4.547

• Języki publikacji: EN

Abstrakty

EN

In the paper, the Lagrange problem given by a fractional boundary problem with partial derivatives is considered. The main result is the existence of optimal solutions based on the convexity assumption of a certain set. The proof is based on the lower closure theorem and the appropriate implicit measurable function theorem.

Słowa kluczowe

EN

fractional partial derivative; fractional boundary problem; existence of optimal solutions; Lagrange problem; lower closure theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 4
• Strony: 547--558
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Majewski Marek

• University of Lodz Department of Mathematics and Computer Science, Banacha 22, 90-238 Lodz, Poland

• https://orcid.org/0000-0003-4542-2592

Bibliografia

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• [4] D. Idczak, A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order, Math. Control Relat. Fields 12 (2022), no. 1, 225–243.
• [5] D. Idczak, R. Kamocki, M. Majewski, Nonlinear continuous Fornasini–Marchesini model of fractional order with nonzero initial conditions, J. Integral Equations Appl. 32 (2020), no. 1, 19–34.
• [6] D. Idczak, K. Kibalczyc, S. Walczak, On an optimization problem with cost of rapid variation of control, J. Austral. Math. Soc. Ser. B 36 (1994), no. 1, 117–131.
• [7] D. Idczak, S. Walczak, On Helly’s theorem for functions of several variables and its applications to variational problems, Optimization 30 (1994), no. 4, 331–343.
• [8] R. Kamocki, Optimal control of a nonlinear PDE governed by fractional Laplacian, Appl. Math. Optim. 84 (2021), no. 2, 1505–1519.
• [9] M. Majewski, On the existence of optimal solutions to an optimal control problem, J. Optim. Theory Appl. 128 (2006), no. 3, 635–651.
• [10] M. Majewski, Stability analysis of an optimal control problem for a hyperbolic equation, J. Optim. Theory Appl. 141 (2009), no. 1, 127–146.
• [11] M.W. Michalski, Derivatives of noninteger order and their applications, Dissertationes Math. (Rozprawy Mat.) 328 (1993), 1–47.
• [12] R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, [in:] J.P. Gossez, E.J. Lami Dozo, J. Mawhin, L. Waelbroeck (eds.), Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics, vol. 543. Springer-Verlag, Berlin-New York, 1976, 157–207.
• [13] S. Walczak, Absolutely continuous functions of several variables and their applications to differential equations, Bull. Polish Acad. Sci. Math. 35 (1987), no. 11–12, 733–744.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)