Opuscula Math. 43, no. 4 (2023), 547-558
https://doi.org/10.7494/OpMath.2023.43.4.547
Opuscula Mathematica
On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order
Abstract. 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.
Keywords: fractional partial derivative, fractional boundary problem, existence of optimal solutions, Lagrange problem, lower closure theorem.
Mathematics Subject Classification: 35R11, 49J20, 49K20.
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- Marek Majewski
https://orcid.org/0000-0003-4542-2592- University of Lodz, Department of Mathematics and Computer Science, Banacha 22, 90-238 Lodz, Poland
- Communicated by Giovanni Molica Bisci.
- Received: 2023-01-15.
- Accepted: 2023-04-27.
- Published online: 2023-06-13.
