ON SOME BOUNDARY VALUE PROBLEMS FOR
EQUATIONS WITH BOUNDARY OPERATORS
OF FRACTIONAL ORDER
Ravshan Ashurov1, Yusuf Fayziev2
1,2 Institute of Mathematics
Academy of Science of Uzbekistan
Student Town, Tashkent - 100174, UZBEKISTAN

Abstract

We deal with boundary value problems for equations with the operator $\frac{\partial^2}{\partial y^2} - A(x,D)$, where $A(x,D)$ is a nonnegative elliptic differential operator and with boundary operators depending on a positive real parameter $\rho$. In particular, boundary conditions can be given through the one-sided Marchaud, Grünwald-Letnikov or Liouville-Weyl fractional derivatives of order $\rho$. We find orthogonality and smoothness conditions on the boundary function, which guarantee both the existence and uniqueness of the classical solutions. Examples of the operator $A(x,D)$ are discussed.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 2
Year: 2021

DOI: 10.12732/ijam.v34i2.6

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