Opuscula Math. 43, no. 4 (2023), 547-558

Opuscula Mathematica

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

Marek Majewski

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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  • Communicated by Giovanni Molica Bisci.
  • Received: 2023-01-15.
  • Accepted: 2023-04-27.
  • Published online: 2023-06-13.
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Cite this article as:
Marek Majewski, On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order, Opuscula Math. 43, no. 4 (2023), 547-558, https://doi.org/10.7494/OpMath.2023.43.4.547

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