Malaya Journal of Matematik

Nonlinear partial completely continuous operators in a partially ordered Banach space and nonlinear hyperbolic partial differential equations

2024-04-11T10:31:18+00:00

We prove a hybrid fixed point theorem for partial completely continuous operators in a partially ordered metric space and derive an applicable hybrid fixed point result in an ordered Banach space as a special case. As an application, we discuss a nonlinear hyperbolic partial differential equation for approximation result of local solutions by constructing the algorithms. Finally, an example is indicated to elaborate the hypotheses and abstract result of this paper.

Mathematical modeling and optimal control of the dynamics of terrorist ideologies

2024-07-20T19:55:19+00:00

We describe the dynamics of the spread of terrorist ideologies within a population, described as an epidemic. The equations of the model are obtained using a contact process, which gives us first-order autonomous non-linear differential equations. Next, the stability of the equilibrium point is established using the basic reproduction number technique; numerical simulations allow us to verify the mathematical results. Finally, optimal control analysis highlights the importance of synergy of action (numbers, equipment, strategy, and training) within the defence and security forces and the importance of patriotism in a nation. In addition, ongoing awareness-raising campaigns are helping to speed up the eradication process.

Analysis and optimal control for SEIR mathematical modeling of COVID-19

2024-03-30T09:49:17+00:00

In this paper a mathematical model of SEIR type is formulated. represented by modeling the coronavirus epidemic. In this present study, we consider a mathematical model that incorporates the whole population and variability in transmission between reported and unreported populations. The global stability of the disease free equilibrium (DFE) point is established. The basic reproduction number R0 is calculated. We introduce into our model two controls which are vaccination of
susceptible humans denoted by u and treatment of infected humans designed by v. In addition, this model takes into consideration the control of contact between infectious individuals and susceptible persons A numerical simulation of the model is made.

Polynomial stability of a Rayleigh system with distributed delay

2024-12-03T02:08:19+00:00

We consider the Rayleigh beam equation with a dynamic control moment with a distributed
delay term in the dynamic control. We establish the strong stability of this system and then
prove that the system with delay has the same rational decay rate as the system without delay.
But we show that it is not exponentially stable. Our contribution is the introduction of the
distributed delay term in the control.

Exponential stability of a porous thermoelastic system with Gurtin Pipkin thermal law and distributed delay time

2024-04-24T14:01:10+00:00

In this paper, we consider a one-dimensional porous thermoelastic system with herditary heat conduction and a distributed delay time acting only on the porous equation, where the heat conduction is given by Gurtin Pipkin law. Existence and uniqueness of a solution are obtained by the use of Hille-Yosida theorem. Then, based on the energy method as well as by constructing a suitable Lyapunov functional, we prove under some assumptions on the derivative of the heat-flux kernel, that the solution of the system decays exponentially without any assumption on the wave speed.

Fractional Hermite-Hadamard type inequalities for co-ordinated convex functions

2024-12-03T01:36:31+00:00

In this paper, we first construct a new integral equality. Using this equality, we establish Hermite-Hadamard type fractional integral
inequalities involving two variables via convexity.

On \(\beta\)-\(\gamma\)-connectedness and \(\beta_{(\gamma,\delta)}\)-continuous functions

2024-12-03T02:08:11+00:00

The purpose of this work is to present the idea of \(\beta-\gamma\)-separated sets, examine their characteristics in topological spaces and then define the notation for \(\beta-\gamma\)-connected and \(\beta-\gamma\)-disconnectedness.\ In addition, the study of topological qualities that involves for \(\beta-\gamma\)-connected spaces via \(\beta-\gamma\)-separated sets.\ An analysis is conducted on the properties of \(\beta-\gamma\)-connected spaces and how they behave under \(\beta_{(\gamma,\delta)}\)-continuous functions.\ We also provide the ideas of \(\beta-\gamma\)-components in a space \(X\) and \(\beta-\gamma\)-locally connected spaces.

On generalized pseudo conformally symmetric manifolds

2024-12-03T02:08:09+00:00

In this paper, a type of Riemannian manifold, namely generalized pseudo conformally symmetric manifold is studied. Several geometric properties of such spaces are studied. By imposing different restrictions on the conformal curvature tensor, we have obtained several properties. If the conformal curvature tensor is harmonic, then the form of the scalar curvature is obtained. Also, the relations among the 1-forms under various conditions are obtained.