Vol. 10, No. 4 (2021): Regular Issue

In this paper, we consider a system of fractional partial differential equations subject to Dirichlet and Neumann boundary conditions. Several sufficient conditions are established for forced oscillation of solutions of such systems. Examples are given to illustrate our main results.

In this manuscript, we establish a class of nonlocal Sobolev-type Hilfer fractional stochastic differential equations driven by fractional Brownian motion, which is a special case of a self-similar process, Hermite processes with stationary increments with long-range dependence. The Hermite process of order 1 is fractional Brownian motion and of order 2 is the Rosenblatt process. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional stochastic systems are established. The derived result in this manuscript is new in the sense that it generalizes many of the existing results in the literature, more precisely for fractional Brownian motion and Poisson jumps case of Sobolev-type Hilfer fractional stochastic settings. Finally, stochastic partial differential equations are provided to validate the applicability of the derived theoretical results.

In this study, the dynamic response of the tension leg platform (TLP) under sea waves excitation is investigated. One establishes the analytical framework consisting of mathematical modeling of TLP taking into account the tendons and the delay. We analyse the stability and determine the physical characteristics of tendon system that allow the system to be always stable. Conditions on the space parameters of the system for which harmonic, subharmonic, superharmonic, combination resonants states are obtained using the multiple time scales method. The results show that the stability area of the system decreases when the delay increases and increases when the damping coefficient increases. Furthermore, increasing the time- delay only increases the value of the maximum amplitude response of the system. However, reasonable selection of the system parameters can effectively reduce the level of vibration of the system.

In this paper, we consider a coupled system of Petrovsky-Petrovsky equations with nonlinear dissipative terms. We proved the existence and stability of solution to the coupled system (1) under some assumptions (7)-(9) based on the work [1]. The approach adopted is the Faedo-Galerkin method. Furthermore, by applying the multiplier method and some weighted integral inequalities, we strictly proved the decay properties (23).

This paper investigates the problem of output feedback $h$-stabilization of nonlinear uncertain systems. We construct an output feedback controller that guarantees global uniform practical $h$-stability of the closed-loop system. Our original results generalize well-known fundamental results: practical stability, practical asymptotic stability and practical exponential stability for nonlinear time-varying systems. Finally, two numerical examples are presented to demonstrate the validity of the proposed method.

Nonlinear systems can be studied by their equivalent linearized systems in the region of equilibrium points. This fact led the study of dynamical systems to be focused near these points. On the contrary Hidden attractors can be found in systems with no equilibrium points, with one stable equilibrium or in systems with lines of equilibrium points. This forces us to ``sail in uncharted waters'' and opens new perspectives in the study of dynamical systems.

A Swimming performance underlies the biomechanical properties and functional morphology of fish fins. In this article, design and realization of a swimming robot propelled by a pair of pectoral fin is implemented. The suggested shape of the pectoral fins is concave; this type of fin provides a simple approach in generating effective hydrodynamic thrust force through only one degree of freedom (1-DOF). Next, we show the effect of varying fin oscillation speed in two phases, the first phase is the power stroke one, where the fins start to push toward the backward of the body, and the recovery phase, where the fins return toward the frontal part of the body. The detailed steps of the robot design are presented and the thrust force exerted by pectoral fins has been evaluated. The robot is consisting of a rigid-body with an elliptical cross-sectional area, which helps in minimizing the water resistance during the thrusting process. Since pectoral fins provide a vital role in the propulsion mechanism of Labridae fish, the proposed model is driven by a pair of concave-shaped fin to simulate labriform mode swimming mechanism. For motion control, we have suggested to use PID controller in order to improve the system performance. The kinematic and dynamic model of a swimming robot has been derived based on Newton-Euler equations, while an evaluation of the total hydrodynamic forces that are exerted on the swimming robot's body is studied via the computational fluid dynamics (CFD) method. The proposed design has been validated theoretically via Solidworks{\textregistered} platform and examined experimentally. The results of the simulation and practical experiments showed the validity and agility of Labriform swimming robot.

In this paper, we present existence and uniqueness of special random impulsive differential evolution equations with nonlocal condition in Hilbert spaces. Moreover we study the stability results for the same evolution equations. Existence and uniqueness results are proved using Banach fixed point theorem where as stability results using fixed point approach and semi group theory. Finally we give some applications of the nonlocal impulsive differential equations as well as evolution equations, which shows the importance of our theoretical results.

Nonlinear difference equations are mostly utilized to describe some natural phenomena. The exact solutions of some models cannot be sometimes extracted. Therefore, investigating the long behaviour of the model may give the future pattern of the respective problem. This article manifests the long behaviour of a seventh order rational difference equation with positive real coefficients. Through this paper, the local stability, global stability, boundedness are obtained analytically and some figures are illustrated to test the accuracy of the solutions. The used technique can be extended to be utilized in solving some higher order difference equations.

The aim of this study is to develop a swimming robot with good steering performance, in which the steering behavior is achieved by one degree of freedom (1-DOF) represented by a two concave-shaped pectoral fins. The steering mechanism adopted here based on differential drive principle. This principle is carried out by varying the right/left fins velocities. Different radii have been achieved with four different cases of velocities. The proposed design has been validated theoretically via Solidworks{\textregistered} platform and proved practically in a physical swimming pool. A minimum turning radius achieved is 0.40 of body length (BL).

The present paper describes a theoretical and an experimental investigation of Clamped-Simply-Clamped-Simply supported isotropic rectangular plates subject to a large amplitudes forced transverse vibration. The theoretical model is based on Lagrange equations and the harmonic balance method which is used to obtain the non-linear algebraic equation of the problem. To examine our results, a test rig is designed and made. Furthermore, an electrodynamic exciter is used to provide the transverse harmonic vibrations, whereas an accelerometer measures the displacements. The approximate analytical solutions are obtained, and the experimental measurements are discussed and compared which are highlight the nonlinear hardening resonance.

A This paper investigates friction-induced instability in a Single Degree-of-Freedom, pseudo-rigid-body representation of a bistable compliant mechanism composed of two sliders connected with a massless rigid link. The friction force is a function of the state variables through Stribeck effect and variable contact force due to the structural nonlinearity of the mechanism. A Constant normal force ensures the mass-belt contact during oscillation. It is shown that the steady-state response of the vibrating mechanism depends on the belt velocity, applied normal load, and stiffness. The applied normal force and belt velocity, as bifurcation parameters, are used to define the number and location of equilibrium points and their corresponding stability.

In this paper we have proposed a three dimensional mathematical model on malaria disease by considering two distinct classes namely susceptible and infected human population and infected mosquito population. Basic reproductive number of the system has been obtained and its relation regarding the behavior of the system has been established. Two control parameters, namely treatment control on infected human population and insecticide control on mosquito populations are applied in the present system. We formulate and solve the optimal control problem considering treatment and insecticide as the control variables. All the theoretical results are verified by some computer simulation works.

We study the discrete-time dynamical systems of a model of wild mosquito population with distinct birth (denoted by $\beta$) and death (denoted by $\mu$) rates. The case $\beta=\mu$ was considered in our previous work. In this paper we prove that for $\beta<\mu$ the mosquito population will die and for $\beta>\mu$ the population will survive, namely, the number of the larvaes goes to infinite and the number of adults has finite limit ${\alpha\over \mu}$, where $\alpha>0$ is the maximum emergence rete.