Sh. A. Alimov, “On the solvability of the Cauchy problem in Gevrey classes for the Weyl fractional derivative equation”, Dokl. RAN. Math. Inf. Proc. Upr., 2025, Volume 523,Pages <nobr>27

MATHEMATICS

On the solvability of the Cauchy problem in Gevrey classes for the Weyl fractional derivative equation

Sh. A. Alimov^ab

^a V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of Uzbekistan, Tashkent
^b National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan

Abstract: An alternative definition of fractional-order Weyl derivatives is given and their effect on functions from the Gevrey classes is studied. Conditions for the solvability of the Cauchy problem in Gevrey classes are found for the Weyl partial differential equation.

Keywords: fractional order Weyl derivatives, Gevrey classes, Cauchy problem.

UDC: 517.9

Presented: B. N. Chetverushkin
Received: 10.05.2025
Revised: 10.06.2025
Accepted: 10.06.2025

DOI: 10.31857/S2686954325030055