In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age-structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup.

Cheng-Hung Hung

Frequently Hypercyclic Semigroup Generated by Some Partial Differential Equations with Delay Operator

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained.

A. S. Nagdy

KH. M. Hashem

H. E. H. Ebrahim

The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection

This study presents families of the fourth-order Runge–Kutta methods for solving a quadratic Riccati differential equation. From these families, the England version is more efficient than other fourth-order Runge–Kutta methods and practically well-suited for solving initial value problems in general and quadratic Riccati differential equation in particular. The stability analysis of the present method is well-established. In order to verify the accuracy, we compared the numerical solutions obtained using the England version of fourth-order Runge–Kutta method with the recently published works reported in the literature. Several counter examples are solved using the present methods to demonstrate their reliability and efficiency.

Wendafrash Seyid Yirga

Fasika Wondimu Gelu

Wondwosen Gebeyaw Melesse

Gemechis File Duressa

Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation

In this paper, we propose an eco-epidemiological mathematical model in order to describe the effect of migration on the dynamics of a prey–predator population. The functional response of the predator is governed by the Holling type II function. First, from the perspective of mathematical results, we develop results concerning the existence, uniqueness, positivity, boundedness, and dissipativity of solutions. Besides, many thresholds have been computed and used to investigate the local and global stability results by using the Routh–Hurwitz criterion and Lyapunov principle, respectively. We have also established the appearance of limit cycles resulting from the Hopf bifurcation. Numerical simulations are performed to explore the effect of migration on the dynamic of prey and predator populations.

Assane Savadogo

Boureima Sangaré

Wendkouni Ouedraogo

A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration

Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird’s digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system’s equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention.

Yustina A. Liana

Mary C. Swai

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

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.

P. Ganesan

G. Palani

John R. Graef

E. Thandapani

Oscillation of Fourth-Order Nonlinear Semi-Canonical Neutral Difference Equations via Canonical Transformations

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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.

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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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Abstract and Applied Analysis - Table of contents 2024

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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.

Abstract and Applied Analysis