Vol. 31 No. 3 (2024)

Open Access

Articles

Article ID: 2439

HOMOTOPY PERTURBATION METHOD TO SOLVE DUFFING-VAN DER POL EQUATION

by BAGAYOGO Moussa, MINOUNGOU Youssouf, NEBIE Abdoul Wassiha, PARE Youssouf

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

In this paper, the Homotopy Perturbation Method (HPM) and the Regular Perturbation Method (RPM) are used to study Duffing-Van der Pol equation. Then we compare the solutions obtained by these two methods.

Open Access

Articles

Article ID: 2440

SUFFICIENCY-TYPE CONDITIONS FOR A TYPE OF STRICTLY DECREASING SOLUTIONS OF LINEAR CONTINUOUS-TIME DIFFERENTIAL SYSTEMS WITH BOUNDED POINT TIME-VARYING DELAYS

by Manuel De la Sen

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

This paper investigates sufficiency-type conditions for strictly decreasing solutions of linear time-delay differential systems subject to a finite number of time-varying bounded point delays. The delay functions are not required to be time-differentiable nor even continuous but simply piecewise bounded continuous. It is not also required for the delay functions at any time instant to be upper-bounded. It is not necessary to have the knowledge of either the delay functions or their lower and upper bounds. It is proved that the supremum of any vector norm of the solution trajectory on consecutive time intervals of finite lengths is strictly decreasing under either stability conditions on the matrix which describes the delay-free dynamics, or on the one which describes the zero-delay auxiliary system, provided in both cases the contribution of the delayed dynamics is sufficiently small related to the convergence abscissas of the above matrices.

Open Access

Articles

Article ID: 2441

ANALYZING AND SIMULATING THE OSCILLATION IN MULTIDIMENSIONAL ODD COMPETITIVE SYSTEMS

by Yury I. Brodsky

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

We consider a multidimensional odd competitive model, which is a generalization to a multidimensional (more than two dimensions) case of both the P. Verhulst logistic model and the A. Lotka and V. Volterra competition model.

Open Access

Articles

Article ID: 2442

HOMOTOPY PERTURBATION METHOD FOR SOLVING A NONLINEAR SYSTEM FOR AN EPIDEMIC

by Nada A. M. Alshomrani, Weam G. Alharbi, Ibtisam M. A. Alanazi, Lujain S. M. Alyasi, Ghadi N. M. Alrefaei, Seada A. Al’amri, Asmaa H. Q. Alanzi

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

This paper solves the SIR-epidemic model utilizing the homotopy perturbation method (HPM). The HPM is applied in a different way in contrast to the HPM in the literature. The current approach uses a new canonical form for the system of the SIR-epidemic. The analytic solution is obtained and compared with the published one, in addition, to the Runge-Kutta numerical method. The results show better accuracy than the corresponding ones.

Open Access

Articles

Article ID: 2443

THE SOME BLAISE ABBO (SBA) PLUS METHOD APPLIED TO FRACTIONAL NONLINEAR TIME SCHRÖDINGER EQUATIONS IN $d$ DIMENSION $(d = 1, 2,$ or $3)$ IN THE SENSE OF CAPUTO

by Oumar MADAI, Germain KABORE, Bakari Abbo, Ousséni SO, Blaise SOME

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

In this paper, we have solved some time fractional Schrödinger equations of order $\alpha$ with $0<\alpha \leq 1$ in dimension $1, 2$ or $3$ in the sense of Caputo by the SBA plus method. This method is based on two principles (successive approximations, and Picard) and the Adomian method. Secondly, it uses a process of rapid convergence in the functional space of the problem posed towards the exact solution, if it exists.

Open Access

Articles

Article ID: 2444

HÖLDER REGULARITY OF SOLUTIONS FOR CERTAIN DEGENERATE PARABOLIC INTEGRO-DIFFERENTIAL EQUATION

by Zongqing Yang, Junhui Xie

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

In this paper, we consider the nonlinear parabolic equation with an integro-differential term. By using classical inequalities and the Moser iteration technique, we establish the estimates for $u$ and $\nabla u$. Then we prove an inequality of Poincare type. As an byproduct of our proof, we derive a Campanato type growth estimate for $u$ which follows from $L^\infty$ estimates of $\nabla u$. Besides, the Hölder continuity of solution is presented by the isomorphism theorem.

Open Access

Articles

Article ID: 2445

FRACTIONAL THERMAL RESPONSE IN A THERMOSENSITIVE RECTANGULAR PLATE DUE TO THE ACTION OF A MOVING SOURCE OF HEAT

by V. R. Manthena, V. B. Srinivas, N. K. Lamba, G. D. Kedar

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

The fractional order theory explores over the field of mathematics and physical sciences as it provides the generalization of non-integer order for derivative and integration. Numerical methods are used to study temperature fields with heat transfer in homogeneous bodies whose thermophysical characteristics depend on the temperature. However, analytical solutions of such problems are needed for qualitative analysis to solve the corresponding problems of thermoelasticity. This study focuses on examining the thermoelastic behavior of a rectangular plate, incorporating time dependent fractional order derivative. Moving line heat source in x-direction is considered for heat conduction analysis. The nonlinearity of the heat conduction equation is dealt using Kirchhoff’s variable transformation. The solution of fractional heat conduction equation (FHCE) is obtained using finite Fourier cosine transform and Laplace transform methods. The obtained solution in transformed domain is expressed in terms of Mittag-Leffler function, trigonometric functions and hypergeometric functions. The effect of time fractional order parameter and velocity on temperature profile and thermal profile is analyzed graphically. During the analysis, it is observed that the inhomogeneous material properties cause the magnitude of profile of thermal characteristics to increase on comparison to that of homogeneous case. Smaller magnitudes of temperature, deflection and stresses are seen for larger values of velocity.

Open Access

Articles

Article ID: 2446

OPTIMAL HARVESTING STRATEGY FOR PREY-PREDATOR MODEL WITH FISHING EFFORT AS A TIME VARIABLE

by Daniel ZAMBELONGO, Moumini KERE, Somdouda SAWADOGO

Advances in Differential Equations and Control Processes, Vol.31, No.3, 2024;

We study a prey-predator model with harvesting where the fishing effort is considered as a function of time. The analysis focuses on the equilibrium points and the optimal harvesting strategy.