TY  - JOUR
ID  - Majewski2023
LB  - Majewski2023
AU  - Majewski, Marek
TI  - On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order
ST  - On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 4
SP  - 547
EP  - 558
DO  - https://doi.org/10.7494/OpMath.2023.43.4.547
UR  - https://doi.org/10.7494/OpMath.2023.43.4.547
AB  - 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.
KW  - fractional partial derivative
KW  - fractional boundary problem
KW  - existence of optimal solutions
KW  - Lagrange problem
KW  - lower closure theorem
SN  - 1232-9274
ER  -