Vol. 28 (2022)

Open Access

Articles

Article ID: 2567

SOME RESULTS ON NONLINEAR MIXED FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

by H. L.Tidke, V. V.Kharat, G. N.More

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

In this paper, we study the existence, uniqueness and other properties of solutions of fractional Volterra Fredholm integrodifferential equation involving Caputo fractional derivative of special class $n-1<\alpha \leq n, \quad n>1$. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality which provides explicit bound on the unknown function. The obtained some results are illustrated through example.

Open Access

Articles

Article ID: 2568

COMMUTATIVITY ASSOCIATED WITH EULER SECOND-ORDER DIFFERENTIAL EQUATION

by Salisu Ibrahim

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

We study commutativity and the sensitivity of the second-order Euler differential equation. The necessary and sufficient conditions for commutativity of the second-order Euler differential equation are considered. Moreover, the stability, the robustness, and the effect due to disturbance on the second-order Euler linear time-varying system (LTVS) are investigated. An example is given to support the results. The results are well verified using the Matlab Simulink toolbox.

Open Access

Articles

Article ID: 2569

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A NICHOLSON-TYPE BLOWFLIES MODEL WITH NONLINEAR DECIMATION TERMS

by Yidi Zhao, Shaowen Liu, Yuqi Cao, Qing Ma, Yan Yan

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

This study considers a Nicholson-type blowflies model with nonlinear decimation terms in a periodic environment. The sufficient condition for this model to have at least two positive periodic solutions is elucidated. Our result is obtained by applying the Krasnoselskii fixed point theorem. Example and its simulations are given to illustrate our result.

Open Access

Articles

Article ID: 2570

LYAPUNOV TYPE INEQUALITIES AND THEIR APPLICATIONS ON AN EIGENVALUE PROBLEM FOR DISCRETE FRACTIONAL ORDER EQUATION WITH A CLASS OF BOUNDARY CONDITIONS

by D. AbrahamVianny, R. Dhineshbabu, A. Selvam

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

The Lyapunov inequality has its importance in the study of broad applications of solutions to differential and difference equations, such as oscillation theory, disconjugacy and eigenvalue problems. This paper is devoted to a new Lyapunov-type inequality for discrete fractional order equations with a class of two-point boundary conditions under the concept of the Riemann-Liouville fractional difference operator. We examine some new results for linear and nonlinear Lyapunov-type inequalities by developing suitable Green’s function and determining their corresponding maximum value for discrete fractional equations. The associated eigenvalue problem is also examined. We provide a couple of examples to demonstrate the applicability of the findings

Open Access

Articles

Article ID: 2571

AN EFFICIENT BLOCK SOLVER OF TRIGONOMETRICALLY FITTED METHOD FOR STIFF ODEs

by Oghonyon JimevwoGodwin, Okunuga SolomonAdewale, Ogunniyi PeterOluwatomi

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

An efficient block solver of trigonometrically fitted method for stiff ODEs has been developed. This block solver utilizes a special trigonometrically fitted method as the basis function approximation with the introduction of varying step, varying order and suitably varying step size. The idea of interpolation and collocation is utilized out via trigonometrically fitted method. Some theoretical properties of block solver are also investigated. To demonstrate the efficiency and accuracy of the method, we solve some examples of stiff ODEs.

Open Access

Articles

Article ID: 2572

INTELLIGENT ADAPTIVE FRACTIONAL-ORDER BACKSTEPPING CONTROL FOR UNCERTAIN NON-LINEAR QUADROTOR

by Lemya Guettal, Chellihi Abdelghani, Mostefa MohamedTouba, Riadh Ajgou

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

An intelligent adaptive fractional-order backstepping control under unknown external disturbances and parameter uncertainties for quadrotor is developed. The developed approach named FCN-FOBC combines fractional-order backstepping control (FOBC) and fuzzy-Chebyshev network (FCN). Initially, the overall control and system tracking are performed using backstepping control (BC). FOBC is designed to advance the convergence speed and control reliability. Second, the FCN is set up to approximate the uncertainties, and a robust term is considered to overcome the problem of FCN approximation errors. Finally, using the Lyapunov theory, the stability of control system is confirmed. The numerical results confirm that the proposed controller has better tracking accuracy and stronger robustness compared to conventional approaches.

Open Access

Articles

Article ID: 2573

ESTIMATION OF PARAMETERS AND STABILITY ANALYSIS OF CORONAVIRUS PANDEMIC

by Poonam Garg, Ritu Arora, Surbhi Madan, Dhiraj KumarSingh

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

Despite ranking amongst the highest in medical systems in Africa and spending a substantial amount on health sector than other African nations, Algeria suffered a major blow in the first wave of the Covid-19 pandemic. Vaccine hesitancy also affected the country adversely in subsequent waves of the disease. This study estimates the number of Covid-19 cases for Algeria in January 2022 using two numerical methods Multi-step Differential Transform Method (MsDTM) and Repeated MsDTM. Stability analysis of the pandemic for the country has also been discussed in the paper.

Open Access

Articles

Article ID: 2574

NUMERICAL BLOW-UP TIME FOR NONLINEAR PARABOLIC PROBLEMS

by Adou KoffiAchille, Diop FatouN., N’Guessan Koffi, Touré KidjégboAugustin

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

In this paper, we analyze numerically some of the features of theblow-up phenomena arising from a nonlinear parabolic equationsubject to nonlinear boundary conditions. More precisely, we studynumerical approximations of solutions of the problem $$\{\begin{array}{l}(\log u(x,t){)}_t=u_{xx}(x,t)+u^{\beta -1}(x,t),(x,t)\in (0,1)\times (0,T),\\ -u_x(0,t)+u^{\alpha }(0,t)=0,t>0,\\ u_x(1,t)+u^{\alpha }(1,t)=0,t>0,\\ u(x,0)=u_0(x)\ge \gamma >0,0\le x\le 1,\end{array}$$ , where $\beta \ge \alpha >1$. We obtain some:conditions under which thesolution of the semidiscrete form blows up in a finite time. Weestimate its semidiscrete blow-up time and also establish theconvergence of the semidiscrete blow-up time to the real one. Finally.we give some numerical experiments to illustrate our analysis.

Open Access

Articles

Article ID: 2575

THE ROBUST PID CONTROLLERS FOR SPECIAL PROCESSES

by Do CaoTrung

Advances in Differential Equations and Control Processes, Vol.28, No., 2022;

The paper presents the tuning method for the PID (Proportional Integral Derivative) of special processes consisting of self-balance with overshoot and self-imbalance with inverse response. It is a continued study of process identification by numerical method and PID controller design based on robust viewpoint. The self-balance process with overshoot is identified by the second order plus dead time with a negative zero (SOPDTZ), while the self-imbalance process with inverse response is modeled by integrating plus first order plus dead time (IFOPDT). To gain robust PID for processes, it requires typical designs. While the SOPDTZ needs a filter of first order lag, the IFOPDT requires to supplement integrating element for controller. For illustration, the detail identification and tuning procedures are presented via an example for each of the processes.