Yu. E. Fayziev, Sh. T. Pirmatov, Kh. T. Dekhkonov, “Forward and inverse problems for the Benney–Luke type fractional equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, Number 9,Pages <nobr>82

Forward and inverse problems for the Benney–Luke type fractional equations

Yu. E. Fayziev^ab, Sh. T. Pirmatov^c, Kh. T. Dekhkonov^d

^a National University of Uzbekistan named after M. Ulugbek, 4 Universitetskaya str., Tashkent, 100174 Republic of Uzbekistan
^b Karshi State University, 17 Kuchabag str., Karshi, 180119 Republic of Uzbekistan
^c Tashkent State Technical University, 2 Universitetskaya str., Tashkent, 100095 Republic of Uzbekistan
^d Namangan State University, 316 Uychi str., Namangan, 160119 Republic of Uzbekistan

Abstract: In the paper, we study direct and inverse problems for fractional partial differential equations of the Benney–Luke type. The conditions for the existence and uniqueness of solutions to the Cauchy problems for a Benney–Luke type equation of fractional order are derived. In addition, the inverse problem of finding the right-hand side of the equation is investigated.

Keywords: Benney–Luke equation, fractional order derivative, direct and inverse problem.

UDC: 517

Received: 18.10.2023
Revised: 27.01.2024
Accepted: 20.03.2024

DOI: 10.26907/0021-3446-2024-9-82-91