Vol. 8, No. 3 (2019): Regular Issue

In this paper, we formulate a set of sufficient conditions for the approximate controllability for a class of second-order neutral stochastic nonautonomous integrodifferential inclusions in Hilbert space. We establish the results with the help of resolvent operators and Bohnenblust-Karlin’s fixed point theorem is to prove the main result. An application is given to illustrate the main result.

In this paper, we discuss the existence, uniqueness and four types of Ulam stability results for a general class of Langevin equations. An illustrate example is given tocheck the applicable of this results.

In this research document, we study the fuzzy (η,ϕ)-mixed vector equilibrium problems. By using the concepts of KKM-mapping, we prove the existence theorem of fuzzy (η,ϕ)-mixed vector equilibrium problems.

We describe some quadratic operators which map the (n−1) - dimensional simplex of idempotent measures to itself. Such operators are divided to two classes: the first class contains all n×n×n - cubic matrices with nonpositive entries which in each n×n dimensional k-th matrix contains exactly one non-zero row and exactly one non-zero column; the second class contains all n×n×n - cubicmatrices with non-positive entries which has at least one quadratic zero-matrix. These matrices play a role of the stochastic matrices in the case of idempotent measures. For both classes of quadratic maps we find fixed points.

The variational problem under consideration is a generalization to higher dimension (n > 2) of a free and constrained deformation of an elastic medium. In the case of the free body the existence of the minimizers of the corresponding energy functional is studied, using standard direct methods. When the elastic medium is subjected to a one parametric force field of the shell, the problem turns to the existence of bifurcation points, where the necessary conditions are also sufficient.

At present chaotic vibrations are the one of the most interesting and explored subjects in nonlinear dynamics. Particularly the routes to chaos in non-smooth dynamical systems are of the special scientists’ interest. Quasiperiodic route to chaos in nonlinear non-smooth discontinuous 2-DOF vibroimpact system is studied in this paper. In narrowfrequency range different oscillatory regimes have succeeded each other many times under very small control parameter varying. There were periodic subharmonic regimes - chatters, quasiperiodic, and chaotic regimes. There were the zones of transition from one regime to another, the zones of prechaotic and postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The chaoticity of obtained regime has been confirmed by typical views of Poincaré map and Fourier spectrum, by the positive value of the largest Lyapunov exponent, and by the fractal structure of Poincaré map.

In this paper, we propose a stochastic viral infection model with general incidence rate. In the proposed model, the stochastic perturbations are modeled by general functions. Further, the global existence and positivity of solutions are investigated. In addition, the stochastic stability of the model is established by using the direct Lyapunov method. Finally, an application of the hepatitis B virus (HBV) is given to validate our theoretical results.

In this paper we develop a non-autonomous predator-prey system with time delay to study the influence of water level fluctuations on the interactions between fish species living in an artificial lake. We derive persistence and extinction conditions of the species. Using coincidence degree theory, we determine conditions for which the system has at least one periodic solution. Numerical simulations are presented to illustrate theoretical results.

An approximate analytical solution to the nonlinear time fractional Boussinesq equation is presented here. Derivative with respect to time variable is replaced with Caputo fractional derivative. The Natural transform method and Adomian decomposition method are employed to obtain the solution. Some test problems are solved to show the accuracy of the proposed method. Behavior of water table head is depicted graphically for various time values.