Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control StrategiesRead the full article
Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.
Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.
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Oscillation of Fourth-Order Nonlinear Semi-Canonical Neutral Difference Equations via Canonical Transformations
The authors present a new technique for transforming fourth-order semi-canonical nonlinear neutral difference equations into canonical form. This greatly simplifies the examination of the oscillation of solutions. Some new oscillation criteria are established by comparison with first-order delay difference equations. Examples are provided to illustrate the significance and novelty of the main results. The results are new even for the case of nonneutral difference equations.
Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems
This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that -Krasnosel’skiĭ mapping associated with -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning -enriched quasinonexpansive mappings have been proved.
Control of the Cauchy System for an Elliptic Operator: The Controllability Method
In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. This is a follow-up to a previous paper on the same subject. Indeed, in an earlier publication, we introduced a regularization method, called the controllability method, which allowed us to propose, on the one hand, a characterization of the existence of a regular solution to the ill-posed Cauchy problem. On the other hand, we have also succeeded in proposing, via a strong singular optimality system, a characterization of the optimal solution to the considered control problem, and this, without resorting to the Slater-type assumption, an assumption to which many analyses had to resort. On occasion, we have dealt with the control problem, with state boundary observation, the problem initially analyzed by J. L. Lions. The proposed point of view, consisting of the interpretation of the Cauchy system as a system of two inverse problems, then called naturally for conjectures in favor of which the present manuscript wants to constitute an argument. Indeed, we conjectured, in view of the first results obtained, that the proposed method could be improved from the point of view of the initial interpretation that we had made of the problem. In this sense, we analyze here two other variants (observation of the flow, then distributed observation) of the problem, the results of which confirm the intuition announced in the previous publication mentioned above. Those results, it seems to us, are of significant relevance in the analysis of the controllability method previously introduced.
Study of the Stability Properties for a General Shape of Damped Euler–Bernoulli Beams under Linear Boundary Conditions
We study in this paper a general shape of damped Euler–Bernoulli beams with variable coefficients. Our main goal is to generalize several works already done on damped Euler–Bernoulli beams. We start by studying the spectral properties of a particular case of the system, and then we determine asymptotic expressions that generalize those obtained by other authors. At last, by adopting well-known techniques, we establish the Riesz basis property of the system in the general case, and the exponential stability of the system is obtained under certain conditions relating to the feedback coefficients and the sign of the internal damping on the interval studied of length .
Caputo Fractional Derivative for Analysis of COVID-19 and HIV/AIDS Transmission
In this study, Caputo fractional derivative model of HIV and COVID-19 infections is analyzed. Moreover, the well-posedness of a model is verified to depict that the developed model is mathematically meaningful and biologically acceptable. Particularly, Mittag Leffler function is incorporated to show that total population size is bounded whereas fixed point theory is applied to show the existence and uniqueness of solution of the constructed Caputo fractional derivative model of HIV and COVID-19 infections. The study depicts that as the order of fractional derivative increase the size of the infected variable decrease as time increase. Additionally, memory effects correspond to order of derivative in the reduction of a number of populations infected both with HIV and COVID-19 infections. Numerical simulations are performed using MATLAB platform.
Global Existence and Decay Rate of Smooth Solutions for Full System of Partial Differential Equations for Three-Dimensional Compressible Magnetohydrodynamic Flows
We focus on the global existence and rates of convergence for the compressible magnetohydrodynamic equations in . We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state in . Rates of convergence for the solution in norm with and its first- and second-order derivatives in norm are obtained, if the initial data belong to with .