On the stability and behavior of solutions in mixed differential equations with delays and advances

2022 ◽  
Author(s):  
Ali Fuat Yeniçerioğlu ◽  
Cüneyt Yazıcı ◽  
Sandra Pinelas
Keyword(s):  
Differential Equations ◽  
The Stability ◽  
And Behavior

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

On the stability of invariant sets of functional differential equations

2003 ◽  
Vol 55 (6) ◽  
pp. 641-656 ◽  
Author(s):  
Stephen R. Bernfeld ◽  
Constantin Corduneanu ◽  
Alexander O. Ignatyev
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Invariant Sets ◽  
Functional Differential ◽  
The Stability

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

SUBSTANTIATION FOR SIMPLIFICATION OF CALCULATION MODELS FOR ASSESSMENT OF THE STABILITY OF ROOF ROCKS

2021 ◽  
pp. 25-36
Author(s):  
Oleksandr Ahafonov ◽  
◽  
Daria Chepiga ◽  
Anton Polozhiy ◽  
Iryna Bessarab ◽  
...  
Keyword(s):  
Differential Equations ◽  
Coal Seam ◽  
Cross Section ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Unit Width ◽  
Distributed Load ◽  
The Stability ◽  
Roof Rocks ◽  
Calculation Models

Purpose. Substantiation of expediency and admissibility of use of the simplified calculation models of a coal seam roof for an estimation of its stability under the action of external loadings. Methods. To achieve this purpose, the studies have been performed using the basic principles of the theory of elasticity and bending of plates, in which the coal seam roof is represented as a model of a rectangular plate or a beam with a symmetrical cross-section with different support conditions. Results. To substantiate and select methods for studying the bending deformations of the roof in the coal massif containing the maingates, the three-dimensional base plate model and the beam model are compared, taking into account the kinematic boundary conditions and the influence of external distributed load. Using the theory of plate bending, the equations for determining the deflections of the coal seam roof in three-dimensional basic models under certain assumptions have a large dimension. After the conditional division of the plate into beams of unit width and symmetrical section, when describing the normal deflections of the middle surface of the studied models, the transition from the partial derivative equation to the usual differential equations is carried out. In this case, the studies of bending deformations of roof rocks are reduced to solving a flat problem in the cross-section of the beam. A comparison of solutions obtained by the methods of the three-dimensional theory of elasticity and strength of materials was performed. For a beam with a symmetrical section, the deflection lies in a plane whose angle of inclination coincides with the direction of the applied load. The calculations did not take into account the difference between the intensity of the surface load applied to the beam. Differences in determining the magnitude of the deflections of the roof in the model of the plate concerning the model of the beam reach 5%, which is acceptable for mining problems. Scientific novelty. To study the bending deformations and determine the magnitude of the roof deflection in models under external uniform distributed load, placed within the simulated plate, a strip of unit width was selected, which has a symmetrical cross-section and is a characteristic component of the plate structure and it is considered as a separate load-bearing element with supports, the cross-sections of this element is remained flat when bending. The deflection of such a linear element is described by the differential equations of the bent axis of the beam without taking into account the integral stiffness of the model, and the vector of its complete displacement coincides with the vector of the force line. Practical significance. In the laboratory, to study the bending deformations and their impact on the stability of the coal seam roof under external loads, it is advisable to use a model of a single width beam with a symmetrical section with supports, the type of which is determined by rock pressure control and secondary support of the maingate at the extraction layout of the coal mine.

scholarly journals Glacial lake drainage: a stability analysis

1997 ◽  
Vol 24 ◽  
pp. 175-180
Author(s):  
Krzysztof Szilder ◽  
Edward P. Lozowski ◽  
Martin J. Sharp
Keyword(s):  
Differential Equations ◽  
Water Flow ◽  
Frictional Heating ◽  
Initial Perturbation ◽  
Tunnel Wall ◽  
Cross Sectional ◽  
Linear Ordinary Differential Equations ◽  
Simplifying Assumptions ◽  
Lake Drainage ◽  
The Stability

A model has been formulated to determine the stability regimes for water flow in a Subglacial conduit draining from a reservoir. The physics of the water flow is described with a set of differential equations expressing conservation of mass, momentum and energy. Non-steady flow of water in the conduit is considered, the conduit being simultaneously enlarged by frictional heating and compressed by plastic deformation in response to the pressure difference across the tunnel wall. With the aid of simplifying assumptions, a mathematical model has been constructed from two time-dependent, non-linear, ordinary differential equations, which describe the time evolution of the conduit cross-sectional area and the water depth in the reservoir. The model has been used to study the influence of conduit area and reservoir levels on the stability of the water flow for various glacier and ice-sheet configurations. The region of the parameter space where the system can achieve equilibrium has been identified. However, in the majority of cases the equilibrium is unstable, and an initial perturbation from equilibrium may lead to a catastrophic outburst of water which empties the reservoir.

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