Abstract
In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.
Highlights
The spectral theory of operators finds numerous uses in various fields of mathematics and their applications.An important part of the spectral theory of differential operators is the distribution of their eigenvalues
This classical question was studied for a second-order operator on a finite interval by Liouville and Sturm
We considered questions on the unique solvability of a mixed problem for a partial differential equation of high order with fractional Riemann-Liouville derivatives with respect to time, and with Laplace operators with spatial variables and with nonlocal boundary conditions in Sobolev classes
Summary
The spectral theory of operators finds numerous uses in various fields of mathematics and their applications. An important part of the spectral theory of differential operators is the distribution of their eigenvalues This classical question was studied for a second-order operator on a finite interval by Liouville and Sturm. G.D. Birkhoff [1,2,3] studied the distribution of eigenvalues for an ordinary differential operator of arbitrary order on a finite interval with regular boundary conditions. The so-called regular case of the Sturm-Liouville problem corresponding to a finite interval and a continuous coefficient of the equation has been studied for a relatively long time and is usually described in detail in the manuals on the equations of mathematical physics and integral equations. Many authors studied fractional differential equations in [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]
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