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Jul 12, 2022Open    Access

Heterogeneity in the Elastic Half-Space (Deformations at Preparation of the Tectonic Earthquake)

Igor P. Dobrovolsky
With the help of Mindlin’s tensor, the problem of heterogeneity in an elastic half-space comes down to the solution system of integrable equations. Different versions of the solution of such systems are considered. The main attention is paid to the solution of integrable equations with small parameters.
Open Access Library J.   Vol.9, 2022
Doi:10.4236/oalib.1108714


Feb 24, 2021Open    Access

Elastic Layer on the Elastic Half-Space: The Solution in Matrixes

Igor Petrovich Dobrovolsky
If to apply bidimensional Fourier’s transform to homogeneous system of equations of the theory of elasticity, then we will receive system of ordinary differential equations. The general solution of this system contains 6 arbitrary constants and allows to solve problems for the layer and the multilayer environment. It is shown that it is convenient to do statement and the solution of such tasks in the matrix form. The task for the layer on the elastic half-space is solved. Ways of inverse of Four...
Open Access Library J.   Vol.8, 2021
Doi:10.4236/oalib.1107191


May 07, 2020Open    Access

On the Stability of Duffing Type Fractional Differential Equation with Cubic Nonlinearity

Nnaji Daniel Ugochukwu, Makuochukwu Felix Oguagbaka, Ezenwobodo Somkene Samuel, Nnaemeka Stanley Aguegboh, Onyiaji Netochukwu Ebube
The purpose of this paper is to study the stability of nonlinear fractional Duffing equation where , by analysing the eigenvalues generated from the system of the given differential equation. Graphical results furthermore show the effect of the damping and nonlinear parameter on the system. Our contribution relies on its application to the choice of hard/soft spring in the mechanism of shock absorbers.
Open Access Library J.   Vol.7, 2020
Doi:10.4236/oalib.1106184


Mar 23, 2020Open    Access

On a Nonlinear Volterra-Fredholm Integrodifferential Equation on Time Scales

Mohammed I. Noori, Akram H. Mahmood
The main aim in this work is to obtain an integral inequality with a clear estimate on time scales. The obtained inequality is used as a tool to investigate some basic qualitative properties of solutions to certain nonlinear Volterra-Fredholm integrodifferential equations on time scales.
Open Access Library J.   Vol.7, 2020
Doi:10.4236/oalib.1106103


Feb 13, 2020Open    Access

Quasiquadrature Solution of the Linear Integral Equations of the Second Kind in the Class of Integrable Functions

Igor Petrovich Dobrovolsky
The analog of the quadrature solution of the equation of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Equations of Fredholm and Volterra are considered. The graphical representation of the solution is discussed. Computing examples show expediency of such approach in appropriate cases.
Open Access Library J.   Vol.7, 2020
Doi:10.4236/oalib.1106069


Sep 12, 2019Open    Access

Quasi-Quadrature Solution of Integral Equations Fredholm of the Second Kind in the Class of Integrable Functions

Igor Petrovich Dobrovolsky
The analog of the quadrature solution of the equation of Fredholm of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Computing examples show expediency of such approach in appropriate cases.
Open Access Library J.   Vol.6, 2019
Doi:10.4236/oalib.1105736


Aug 29, 2019Open    Access

The Power Integrations of Trigonometric and Hyperbolic Functions

Ahmed M. Ali, Omar M. Abd-Alkanee
For importance of the trigonometric integrals, we have in this paper finding a series of power, some of trigonometric functions that did not exist before in the first section. As shown in the Section two, where, the integration of trigono-metric function with power n has been achieved and approved, this result is considered as the first achievement. while in the third section we find integrals
...
Open Access Library J.   Vol.6, 2019
Doi:10.4236/oalib.1105618


Dec 15, 2017Open    Access

Collocation Technique for Numerical Solution of Integral Equations with Certain Orthogonal Basis Function in Interval [0, 1]

O. L. Babasola, I. Irakoze
This paper is concerned with the construction of a class of polynomial orthogonal with respect to the weight function w(x)=1-x2 over the interval [0,1]. The zeros of these polynomials were employed as points of co
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Open Access Library J.   Vol.4, 2017
Doi:10.4236/oalib.1104050


Dec 22, 2014Open    Access

Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments

Guangjie Liu, Chengyong Wang
This paper investigated oscillatory properties of solutions for nonlinear parabolic equations with impulsive effects under two different boundary conditions. By using integral averaging method, variable substitution and functional differential inequalities, we established several sufficient conditions. At last, we provided two examples to illustrate the results.
Open Access Library J.   Vol.1, 2014
Doi:10.4236/oalib.1101168


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