Vol. 6, No. 4 (2017): Regular Issue

In this paper we study the existence of solutions for a class of semilinear fractional differential equations with nonlocal conditions and involving abstract Volterra operators. The existence of an optimal solution for a class of fractional control problem involving Caputo fractional derivatives is obtained. An example is presented to illustrate our main result.

Sufficient conditions for boundary controllability of time varying delay differential systems of fractional order with nonlocal condition in Banach space are established. The results are obtained by using fixed point theorems. An example is provided to illustrate our results.

In this paper we consider a family of fifth-order Korteweg-de Vries equations with time-dependent coefficients and linear damping term. By using the multiplier method of Anco and Bluman we determine all the low order conservation laws.

This paper is devoted to proving the existence of solutions to frac- tional impulsive q-difference equations. An approach based on the Schaefer’s fixed point theorem to prove existence of the solution is presented. There is almost no work on the existence results for im- pulsive fractional q-difference equations. The main aim of this paper is to close this gap.

Both oscillatory and chaotic convection are studied using weakly non- linear and nonlinear theories. A weakly nonlinear analysis was em- ployed to derive Complex Ginzburg-Landau amplitude equation. The time dependent temperatures of the plates are considered in three ways, out of phase, lower plate and in phase modulation. The first two temperature profiles show impact on heat and mass transfer and the dynamics of the problem. It is also found that in-phase tempera- ture modulation has negligible effect; while out of phase modulation and only lower plate modulation have significant effects on heat and mass transport. Heat mass transfer is measured in the system in terms of the Nusselt and Sherwood numbers. Heat mass transfer be- comes rapid on either increasing Rs,Pr, λ, δ or decreasing Q, Γ, ε, Ω. Further, the Lorentz model has been simplified under modulation ef- fect, and it is observed that, the chaotic nature of the system may altered with modulation. Unstable solution for OPM, stable solu- tions for IPM, LBMO is found depending on the suitable values of modulation parameters.

Hysteresis is a nonlinear behaviour, which has been considered very hard to model. It is commonly found in actuators and sensors, involving quasi-static memory effects between input and output variables. Usually, continuous time models are used to model this feature. However, polynomial NARX model has come up as an alternative to model this behaviour. Since NARX models are discrete-time models, it is important to verify how the sampling rate interfere in obtaining the mathematical model. Further, frequently continuous-time models are used as a bench test, to generate data for identification of several nonlinear behaviour, including hysteresis. This paper investigates how the sampling rate and discretization methods affects the parameter identification of a NARX model for a system with hysteresis. Improved Euler and fourth order Runge-Kutta methods are applied in a Bouc-Wen model for a magneto-rheological damper, which is used as a system to be identified by a NARX model, considering the above mentioned scenario. Least-square based technique is used in this work to estimate model parameters.

This paper considers a mariner under PDμ controller and analyses the effects of controller parameters on the yaw rate by using the Nomoto model. The Nomoto model describing the time evolution of the yaw rate of the steering dynamics of a mariner is reduced to an asymmetric Duffing oscillator with fractional order derivative. Under the approximation of calm water, the steady behavior of the mariner shows an “imperfect” supercritical pitchfork bifurcation. Region of safe behavior is identified and strategy to reduce the yaw rate by an appropriated selection of controller parameters are discussed. The frequency analysis of the mariner shows the prominence of hysteresis is reduced for small order of the fractional derivative as well as the amplitude of the yaw rate. Evidence of chaotic response is illustrated using robust chaotic indicators such as the Lyapunov exponent and the fast Fourier transform.

This paper considers a mariner under PDμ controller and analyses the effects of controller parameters on the yaw rate by using the Nomoto model. The Nomoto model describing the time evolution of the yaw rate of the steering dynamics of a mariner is reduced to an asymmetric Duffing oscillator with fractional order derivative. Under the approximation of calm water, the steady behavior of the mariner shows an “imperfect” supercritical pitchfork bifurcation. Region of safe behavior is identified and strategy to reduce the yaw rate by an appropriated selection of controller parameters are discussed. The frequency analysis of the mariner shows the prominence of hysteresis is reduced for small order of the fractional derivative as well as the amplitude of the yaw rate. Evidence of chaotic response is illustrated using robust chaotic indicators such as the Lyapunov exponent and the fast Fourier transform.

The spontaneous formation of a wide variety of natural patterns with different shapes and symmetries in many physical and biological systems is one of the deep mysteries in science. This article describes the physical principles underlying the formation of various intriguing spatio-temporal patterns in Nature with special emphasis on some biological structures. We discuss how the spontaneous symmetry breaking due to diffusion driven instability in the reaction dynamics lead to the emergence of such complicated natural patterns. The mechanism of the formation of various animal coat patterns is explained via the Turing-type reaction-diffusion models.