Vol. 11, No. 4 (2022): Regular Issue

Present study analyzes the phenomena of entropy generation of magneto micropolar nanofluid through microchannel with constant pressure gradient. The energy efficiency has been analyzed via entropy generation of the system. The dimensionless two-point boundary value problem acquired from governing equations via dimensionless variables. The nonlinear system is tackled by using Runge-Kutta-Fehlberg scheme. An appropriate comparison has been made with previously published results in the literature as a limiting case of the considered problem. The comparison confirmed an excellent agreement. Influences of flow controlling parameters on velocity, microrotation, temperature, entropy generation number and Bejan number profiles are exemplified quantitatively through graphs. From the comprehensive parametric study, it is established that the entropy production can be improved with Joule heating, convective heating and viscous dissipation aspects.

In current years, fractional calculus has received much attention because it can include memory effect to the inventory model. In the paper, fractional order derivative and integration have been applied to include the memory dependency to the polynomial type demand rate inventory model under the fuzzy environment. The advantage of fractional order derivative and integration have been applied to the EOQ model taking fuzzy environment. Inventory cost parameters, for example holding cost, purchasing cost and ordering cost are thought to be triangular fuzzy numbers. Two type memory indices (i) differential memory index, (ii) integral memory index have been established where differential memory index is associated with the fractional order derivative and integral memory index is associated with the fractional order integration. Defuzzification has been considered using graded mean integration method and signed distance method. Numerical examples and graphical presentations are considered to explain importance of the work.

The paper is devoted to the study of existence and exponential stability of mild solutions of random impulsive differential evolution equations. The results are obtained using Leray-Schauder alternative fixed point theorem. Furthermore Exponential stability of the mild solution is established with certain sufficient conditions. An application is provided to illustrate the theory.

The concern of the present article is to look at the impacts of thermal stratification and heat transfer on two dimensional, laminar, incompressible nanofluid flow over an unsteady stretching sheet.~The influence of thermal stratification added to the energy equation and temperature boundary condition.~The nanoparticles sorted out here are Barium, and Zinc Ferrite.~The base liquid as taken as water.~The governing system of equations is reduced in the system of nonlinear differential equations and solved numerically.~The influence of the thermal stratification parameter, electric field parameter on temperature, skin-friction, heat transfer rates has examined.~The comparison made with the available outcomes in the literature and present outcomes is adequate concurrence with the literature's findings for different estimations.~A bit of the results shows that with an increase in thermal stratification parameter temperature profile decreases; subsequently, heat transfer rate increases.~We also conclude an increase in the nanoparticle volume fraction that the heat transfer rate increases from Barium to Zinc ferrite.

This paper explores the existence of solutions for the system of impulsive integrodifferential equation with anti-periodic boundary value problems on time scales. Some sufficient conditions for the existence of solutions are established by using Schauder's fixed point theorem and Schaefer fixed point theorem.

For any graph $G$, we use $P(G, \lambda)$ to denote the the chromatic polynomial of $G$. Two graphs $G$ and $H$ are said to be equivalent, simply denoted by $G\sim H$, if $P(G, \lambda)=P(H, \lambda)$. Let $[G]=\{H|H\sim G\}$. $G$ is said to be chromatically unique if $[G]=\{G\}$. Let $K(n, n, n)$ be the complete tripartite graph with each part vertex set having $n$ vertice and $S$ be an edge set of $s$ edges in $K(n, n, n)$. In this paper, we give some chromatically unique tripartite graphs obtained by deleting some edges from $K(n, n, n)$ .

In this article, a predator-prey model has been developed incorporating two important factors, namely, the fear factor and the stage structure on both species. It is considered that the growth rate of the prey population is suppressed due to the fear of adult predators. Two separate compartments such as prey and dead prey of prey population have been considered. Also, predator population has been classified into three subpopulations such as suckling in predator population, juvenile and adult predator population. Different possible biologically meaningful equilibrium points are evaluated. Local stability of our proposed system around these equilibrium points has been investigated. Global stability of the interior equilibrium point has also been studied. Hopf bifurcation analysis of the system around the interior equilibrium point with respect to fear factor $(k)$ has been investigated. Direction and stability of Hopf bifurcation are also investigated. It is found that the fear factor has the ability to stabilize the system. It is also found that the higher rate of consumption of dead prey by juvenile and adult predator may make the system unstable. Again, it is also found that the rate of transfer of predator from suckling stage to juvenile stage can change the system dynamics. Some numerical simulation results are presented to validate analytical findings.

An eco-epidemiological predator-prey model with Holling type-II functional response is proposed in this work. In the presence of disease, the prey population has been divided into two subpopulations: susceptible and infected prey. The predator can access the full healthy prey population for hunting but a predator is provided with a fraction of the infected prey as infected prey refuge term is incorporated here. Also, a strong Allee effect in susceptible population is introduced to make the model more realistic. Boundedness and positivity of the system strengthen that the proposed model is well-posed. The strong Allee threshold and the infected refuge parameter have been taken as the key parameters to control the system dynamics. The numerical simulation gives that regulating the refuge parameter can turn an oscillating state into a stable coexistence state. Also, the system changes its dynamics from two interior equilibrium points to no interior point when this refuge parameter crosses the saddle-node bifurcation threshold. Besides, the strong Allee threshold can also change the dynamics of a system from oscillating state to steady-state through Hopf bifurcation.

Platform-vibrators are the main molding equipment in the production of precast concrete elements. It is designed for compaction and molding of concrete products. We have created a mathematical model of a platform-vibrator with shock which is used for the manufacture of large elements. The created model corresponds to a strongly nonlinear non-smooth discontinuous 2-DOF vibro-impact system with soft impact. The simulation of soft impact with linear force and nonlinear force corresponding to qusistatic contact Hertz law is compared. The analysis of dynamic behaviour when changing the exciting frequency is performed. The zones of periodic motion, hysteresis, transient chaos, and a boundary crisis on its right border are shown. The chaoticity of the movement is confirmed by the typical form of phase trajectories, Poincar\'{e} maps, Foureir spectra, the positive sign of Lyapunov exponent, the fractal structure of Poincar\'{e} map, and the specific form of wavelet coefficients surface and its projection.

In this article, we prove the existence, uniqueness and some stability results for fractional integro-differential equation of reconstruction of the unknown time-dependent boundary function $\gamma \left( t\right) $ from an additional integral measurement $\theta \left( t\right) =\int_{\Omega }I^{1-\alpha }\left( u\left( t, x\right) \right) dx$ by the use of Rothe time discretization. Numerical experiments are given to illustrate the results.

A Duffing type oscillator simulates a micromechanical resonator with electrostatic force on both sides. The system, concerning the amplitude of the external excitation and the damping parameter, has rich dynamics that contain regular (periodic and semi- periodic) and chaotic oscillations. Melnikov's function proves the existence of homoclinic chaos.

We consider a family of Hamiltonian systems with homogeneous potentials $V_n$ of degree $n$. These systems are known to be Liouville integrable and their first integrals of motion are known. We examine first the easiest case where the potential function is a cubic polynomial and we find the separation coordinates. After we prove that all the systems in the family can be completely solved in quadratures using these new coordinates.

In this paper we consider following (p,q)-Laplacian system $$ \left\{ \begin{aligned} & -\Delta _{p}u=\lambda l\left( x\right) u^{p-1}-f_{1}\left( u,v\right) -au^{-\alpha _{1}}v^{\beta _{2}}\ \text{in }\Omega , \\ & -\Delta _{q}v=\mu k\left( x\right) v^{q-1}-f_{2}\left( u,v\right) -bu^{\alpha _{2}}v^{-\beta _{2}}\text{ in }\Omega , \\ & u=v=0\text{ on }\partial \Omega , \end{aligned} \right. $$ where $\Omega $ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary $\partial \Omega $, $\lambda $ and $\mu $ are a positive parameters and $a,$ $b$ are a positive constant. By using the method of sub-supersolution we discuss the existence of positive solution.

In this work, we propose an approximate solution for the nonlinear Schr\"{o}dinger with harmonic oscillator by fractional calculus with Caputo definition. It is observed that the nonlinear Schr\"{o}dinger equation in one and two dimensions effect on the behavior of the wave function, the result shows the technique is highly encouraging and efficient.

This paper focuses on the problem of exponential stability of certain classes of dynamic perturbed systems on time scales using time scale versions of some Gr\"{o}nwall-Bihari type inequalities.We prove under certain conditions on the nonlinear perturbations that the resulting perturbed nonlinear initial value problem still acquire exponential stable, if the associated linear system has already owned this property. The paper ends up with two illustrative examples to highlight the utility of our results.