A new class of fractional impulsive differential hemivariational inequalities with an application

We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS

In this paper, we develop a numerical method for the solution of nonlinear fractional integral equations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain conditions, we also prove the uniqueness and existence as well as Hyers–Ulam (HU) stability of the solution. With the help of the mentioned technique, the considered problem is transformed to a system of algebraic equations which is then solved for the required results by using Broyden algorithm. To check the validation and convergence of the proposed technique, some examples are given. For different number of collocation points (CPs), maximum absolute and mean square root errors are computed. The results show that for solving these equations, the HWCT is effective. The convergence rate is also measured for different CPs, which is nearly equal to [Formula: see text].

On the problem of simulation of influence flooded compartment on the dynamics of the ship's navigation.

В статье рассматривается возможность применения имеющихся в настоящее время решений задачи о влиянии динамического переливания жидкости в аварийных отсеках 2-й категории или успокоительных цистернах на качку судна в системах имитационного моделирования динамики плавания аварийных судов. Существующие решения получены в интересах исследования качки в частотной области и формально могут быть перенесены во временну́ю область, отвечающую существованию имитационных моделей, посредством обратного преобразования Фурье, что связано с определенными затруднениями. В работе показано, что при определенной формулировке гидродинамической задачи о колебаниях жидкости в отсеке или цистерне во временно́й области могут быть использованы непосредственно исходные уравнения. Выполнены расчеты, подтверждающие корректность такого подхода с позиций обеспечения устойчивости решения задачи и физической адекватности результатов реально наблюдаемым процессам. The article discusses the possibility of using the currently available solutions to the problem of the effect of dynamic fluid overflow in emergency compartments of the 2nd category or damping tanks on the pitching of a ship in systems for simulation of the dynamics of navigation of damaged ships. The existing solutions were obtained in the interests of studying the pitching in the frequency domain and can formally be transferred to the time domain corresponding to the existence of simulation models by means of the inverse Fourier transform, which is associated with certain difficulties. It is shown in the work that with a certain formulation of the hydrodynamic problem of fluid oscillations in a compartment or tank in the time domain, the original equations can be used directly. Calculations have been performed that confirm the correctness of this approach from the standpoint of ensuring the stability of the solution to the problem and the physical adequacy of the results to the actually observed processes.

Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity

The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution.

Embeddings of integrable models in supergravity and their perturbative stability

We discuss the perturbative stability of an AdS 3 non-supersymmetric solution of the type-IIB supergravity, whose internal geometry is given by the direct product of a round three-sphere and two λ-deformed factors based on the coset CFTs SU(2)/U(1) and SL(2, ℝ)/SO(1,1). This solution admits a two-dimensional parametric space spanned by the inverse radius of the AdS 3 and the deformation parameter λ. Reality of the background imposes restrictions on the values of these parameters. Further limitations on the values of the inverse radius and the parameter λ arise after requiring the stability of the solution. Our approach relies on the study of scalar perturbations around the AdS 3 vacuum of a three-dimensional effective theory. This reveals the existence of a region in the parametric space where the Breitenlohner-Freedman bound is not violated.

Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

Nonlinear Analysis of Cable Net Structures

Objective: To present a methodology for implementing in MathCAD, a based on force densities for analytical form finding to three-dimensional cable net structures subjected to static loading. It is desired that the routines present a stability of the solution algorithm and fast convergence. Methodology: Theoretical background of the cable net structures behavior and FDM are first introduced. Then, a series of MathCAD routines are created to perform the nonlinear analysis of cable net structures. Finally, a well-documented cable net structure example found in the literature, and the results from a cable net software are used as a way to validate the output results provided by the created MathCAD routines. Results: The simulation results show that the proposed methodology implemented in MathCAD can accurately estimate the free nodes displacements and cable forces of 3D cable net structures subjected to vertical and horizontal static loading. Conclusions: This paper has demostrated that the propossed methodology is consistent when comparing with the results given in the reference paper and the used software. Stability of the algorithms is controlled and no numerical issues was presented during the analyzed examples thus, divergence complications were not found. The routines provided a clear way to visualize the assumptions, methods, and critical data obtained in the geometric analysis of cable net structures helping to overcome the inherit limitations of commercial packages.

An Inventory Model for Perishable Goods with Partial Backlogging of Shortages

This study illustrates inventory associated with deteriorating items. Nowadays the incident deterioration has a major impact on the preservation of goods in terms of handling inventory. The significant effect of deterioration has been observed on volatile liquids, fish, vegetables, etc. Here a mathematical model is presented incorporating the effect of deterioration. The model has been developed on an infinite time horizon. The shortage is allowed and backlogged partially. We aim to find out lot-size and back-ordered quantities in order to minimize the total average cost. In support of the proposed model, a numerical example has been provided. The stability of the solution of that example has been confirmed by performing a sensitivity analysis of key parameters. A graphical representation of cost function regarding decision variables has been displayed.

Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative

In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.