Inverse Problem of Determination of the Right-Hand Side of an Equation with Fractional Derivatives In Weight Distributions

2021 ◽  
Vol 258 (4) ◽  
pp. 408-421
Author(s):  
А. О. Lopushansky ◽  
H. P. Lopushanska
Keyword(s):  
Inverse Problem ◽  
Fractional Derivatives ◽  
Right Hand ◽  
Weight Distributions ◽  
The Right

On the determination of the right-hand side in a parabolic equation

2012 ◽  
Vol 62 (11) ◽  
pp. 1672-1683 ◽  
Author(s):  
A. Ashyralyev ◽  
A.S. Erdogan ◽  
O. Demirdag
Keyword(s):  
Parabolic Equation ◽  
Right Hand ◽  
The Right

Reconstruction of a convolution operator from the right-hand side on the semiaxis

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Anatoly F. Voronin
Keyword(s):  
Inverse Problem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Explicit Formulas ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Operator Kernel ◽  
Problem Solvability

AbstractIn this paper, a Volterra integral equation of the first kind in convolutions on the semiaxis when the integral operator kernel and the right-hand side of the equation have a bounded support is considered. An inverse problem of reconstructing the solution to the equation and the integral operator kernel from values of the right-hand side is formulated. Necessary and sufficient conditions for the inverse problem solvability are obtained. A uniqueness and stability theorem is proved. Explicit formulas for reconstruction of the solution and kernel are obtained.

Approximations by multivariate perturbed neural network operators

2017 ◽  
Vol 15 (03) ◽  
pp. 413-432 ◽  
Author(s):  
George A. Anastassiou
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Activation Function ◽  
Jackson Type ◽  
Partial Derivatives ◽  
Right Hand ◽  
Hidden Layer ◽  
The Right ◽  
Derivatives Of

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.

scholarly journals On an Identification Problem on the Determination of the Parameters of the Dynamic System

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Dossan Baigereyev ◽  
Nevazi Ismailov ◽  
Yusif Gasimov ◽  
Atif Namazov
Keyword(s):  
Inverse Problem ◽  
Dynamic System ◽  
Calculation Method ◽  
Identification Problem ◽  
Quadratic Functional ◽  
Nonlinear Ordinary Differential Equations ◽  
Quasilinearization Method ◽  
The Right ◽  
The Given

An inverse problem is considered for the determination of the parameters, involved in the right-hand side of the system of nonlinear ordinary differential equations by given initial and final conditions. The solution of the problem is reduced to the minimization of the quadratic functional, which indeed is a deviation of the value of the solution from the given values at the end points. Using the quasilinearization method a calculation method is proposed to the solution of the considered problem. The application of this method is demonstrated on the example of the determination of the hydraulic resistance in the tubes.

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