On a boundary-value problem for the parabolic-hyperbolic equation with the fractional derivative and the sewing condition of the integral form

2014 ◽  
Author(s):  
Abdumauvlen S. Berdyshev ◽  
Erkinjon T. Karimov ◽  
Nazgul S. Akhtaeva
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Integral Form

scholarly journals On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1030
Author(s):  
Abdumauvlen Berdyshev ◽  
Alberto Cabada ◽  
Erkinjon Karimov
Keyword(s):  
Boundary Value Problem ◽  
Integral Representation ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Functional Space ◽  
Integral Form ◽  
Characteristic Line ◽  
Nuclear Operator ◽  
Local Boundary ◽  
Strong Solvability

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problem.

scholarly journals ON A BOUNDARY VALUE PROBLEM WITH NONLOCAL IN TIME CONDITIONS FOR A ONE-DIMENSIONAL HYPERBOLIC EQUATION

2017 ◽  
Vol 19 (6) ◽  
pp. 31-39
Author(s):  
S.V. Kirichenko
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Form ◽  
Generalized Solution ◽  
One Dimensional

In this article, the boundary value problem for hyperbolic equation with nonlocal initial data in integral form is considered. Existence and uniqueness of generalized solution are proved.

One method for the boundary value problem eigenvalues calcuating for a second-order differential equation with a fractional derivative

2019 ◽  
Vol 10 (01) ◽  
pp. 1941004
Author(s):  
Temirkhan Aleroev ◽  
Hedi Aleroeva ◽  
Lyudmila Kirianova
Keyword(s):  
Differential Equation ◽  
Perturbation Theory ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Linear Operators

In this paper, we give a formula for computing the eigenvalues of the Dirichlet problem for a differential equation of second-order with fractional derivatives in the lower terms. We obtained this formula using the perturbation theory for linear operators. Using this formula we can write out the system of eigenvalues for the problem under consideration.

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