Abstract and Applied Analysis

We propose new sufficient conditions for the exponential stability of a class of nonlinear delay difference equations with continuous time (DECT). The above conditions provide a direct estimation of the exponential decay rate of the system. As applications, explicit sufficient conditions for the exponential stability of the zero solution of continuous difference equations with “maxima” are given.

In this study, we have introduced the neutrosophic generalized β−J contraction as a generalization of the neutrosophic J-contraction with admissible mappings. Sufficient conditions for the existence and uniqueness of the fixed points for a neutrosophic generalized β−J contraction are derived in complete strong neutrosophic metric spaces (SNMSs). An application is given to support the main result. MSC2020 Classification: 47H10, 45D05, 54H25

In this article, we prove the existence of at least one solution to the nonresonant higher-order p-Laplacian boundary value problem of the form: σrφpun−1r′+gr,ur,u′r,…,un−1r=0,r∈0,∞, ui0=0, i=0,1,2,…,n-2, limr→∞σrφpun-1r=∑j=1nβjσηjφpun−1ηjwith the nonresonant condition ∑j=1nβj≠1. We employ the Leray–Schauder continuation principle and some apriori estimates to obtain our result. MSC2010 Classification: 34B10, 34B15

The focus of this paper is the investigation of shape optimization problems with operators such as fractional Laplacian and p-Laplacian operators, that is, −Δs and −Δps, where 0<s<1 and p≥2. In the admissible set of s− quasi-open, the existence of optimal shape is proved for shape derivative of the functional FΩ=fΩ,uΩ, where uΩ represents the solution of the fractional operators.

This paper focuses on existence and uniqueness of common fixed points for a pair of self-mapping satisfying generalized rational type ϑ,ψ,φ-weak contractive condition in which one of the mapping is α-admissible with respect to the other and weakly compatible mappings in the framework of b-metric spaces. The results presented herein generalize and improve some well-known results in the existing literature. Furthermore, we draw some corollaries from our results and provide an example for illustrating the validity of our findings. As an application of our result, we discuss the existence of a solution to a fractional order differential equation.

This article discusses a few different types of singular integral equations of the convolution type with Carleman shift in class {0}. By using the theory of Fourier analysis, these equations under consideration are transformed into Riemann–Hilbert boundary value problems for analytic functions with shift and discontinuous coefficients. For such problems, we propose a method different from the classical ones, and we obtain the analytic solutions and the conditions of Noether solvability. MSC2010 Classification: 45E10, 45E05, 30E25

The periodical dynamics of a G0 cell cycle model of pluripotential stem cells is analyzed by DDE-Biftool software. The cell cycle model is impressed by modeling the optional choice of Hill function, which is benefited by Fourier transformation. The cell cycle is based on DDEs with distributed time delay, in which the kernel function is denoted by Gamma-distribution expression. Hopf bifurcation of the linear version of the cell cycle model with distribution time delay is analyzed analytically. The periodical solution continuation is simulated by the artificial handbook of DDE-Biftool software. With the discrete time delay, the complex behavior of adding-period bifurcation and period-doubling bifurcation are simulated. With distribution time delay, the continuation work of the homoclinic solution is done, and the homoclinic bifurcation line crosses the generalized Hopf point nearly. JEL Classification: 34C25, 34K18, 37G15

The paper proposes a viscosity approximation algorithm for approximating fixed points. The study in this paper demonstrates that without having the prior estimations of operator norm and semicompactness of one-parameter semigroups of nonexpansive mappings, the algorithm converges strongly to the solution of split equality generalized mixed equilibrium problem (SEGMEP). MSC2010 Classification: Primary 47H10, 47H09, 47J05, 47J25, 54H25

This paper presents a compartmental model in ordinary differential equations of tuberculosis (TB) disease dynamics in a prison population, which is calibrated to reflect the unique conditions of the Democratic Republic of Congo. Data are sourced from various sources of statistics that are publicly available and also from other modeling publications. The model is utilized to determine the optimal roll-out strategy for a combination of intervention strategies in TB control in a prison population. The two control functions both address treatment but are linked to different infection classes, making them distinct functions of time. Numerical simulations reveal that without well-planned control measures, TB remains endemic. However, optimal control strategies can potentially eliminate the disease, provided the influx of TB-infected prisoners is controlled. Implementing these strategies can significantly reduce the number of infectious TB cases while minimizing treatment costs. MSC2020 Classification: 92D30, 34K20

In the paper, we give several limit case Euler–Abel type transforms for alternating cosine and sine series. Making use of a property of the operator of generalized difference, applied in the transforms, we give transforms for nonalternating series, which are stronger than similar transforms for alternating series given earlier. MSC2020 Classification: Primary 65B10, Secondary 42A38, 40A25, 40A05

In this article, the solutions of Bessel’s differential equations (DEs) by variable change method are formulated. To do so, we have considered the first and second kind of Bessel’s functions which are obtained as solutions of Bessel’s equations and it is used to determine the solutions of the lengthening pendulum (LP). To solve the given equations, we have used Frobenius theorem and the gamma function and hence, apply the obtained results to solve the LP. The finding reveals that Bessel’s functions establish the solutions of LP equations. The solutions obtained for lengthening the pendulum are illustrated graphically using the computer software of MathLab. The graphical results show that the sinusoidal wave natures are compressed or extended based on the chosen parameter k. Finally, it is concluded that the obtained method gives an effective, efficient, and systematic method.

We examine a linear q−difference differential equation, which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q−analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm logt and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q−difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey-type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q−Gevrey type growth.

For q>1, a new Green’s function provides solutions of inhomogeneous multiplicatively advanced ordinary differential equations (iMADEs) of form yNt−Ayqt=ft for t∈[0,∞). Such solutions are extended to global solutions on ℝ. Applications to inhomogeneous separable multiplicatively advanced partial differential equations are presented. Solutions to a linear free forced q-advanced Schrödinger equation are obtained, opening an avenue to applications in quantum mechanics. New q-Mittag-Leffler functions qEα,β and ΥN,p govern the allowable decay rate of the inhomogeneities ft in the above iMADE. This provides a refinement to standard distribution theory, as we show is necessary for this study of iMADEs. A q-Fredholm theory is developed and related to the above approach. For ft whose antiderivatives provide eigenfuntions of the noncompact integral operator K below, we exhibit solutions of the iMADE. Examples are provided, including a certain class of Dirichlet series.

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.

The purpose of this paper is to introduce q-Post–Widder operators based on a new parameter and study their approximation properties. The moments and central moments are investigated. And some local approximation properties of these operators by means of modulus of continuity and Peetre’s K-functional are presented. Furthermore, the rate of convergence for these operators is obtained. Weighted approximation and the quantitative q-Voronovskaja type theorem are discussed. Finally, numerical illustrative examples have been given to show the convergence of these newly defined operators.

In this study, we proposed and analyzed a nonlinear deterministic mathematical model of malaria transmission dynamics. In addition to the previous approaches, we incorporated the class of aware people and other control measures. We established the wellposedness of the model, and the asymptotic behavior of the solutions is rigorously studied depending on the basic reproduction number R0. The model system admits two equilibrium points: disease-free and disease-persistent equilibrium points. The analytical result of the model system revealed that the disease-free equilibrium point is both locally as well as globally asymptotically stable whenever R0<1 while the disease-persistence equilibrium point is globally asymptotically stable whenever R0>1. Moreover, the forward bifurcation phenomenon of the model system for R0=1 was analyzed by using center manifold theory. A sensitivity analysis of the basic reproduction number was performed to identify parameters that will cause to trigger the transmission of malaria disease and should be targeted by control strategies. Then, the model was extended to the optimal control problem, with the use of three time-dependent controls, namely, preventive measures(treated bednets and indoor residual spraying), continuous awareness campaigns to susceptible individuals, and treatment for infected individuals. By using Pontryan’s maximum principle, necessary conditions for the transmission of malaria disease were derived. Numerical simulations are illustrated by using MATLAB ode45 to validate the theoretical results of the model. The numerical findings of the optimal model suggested that integrated control strategies are better than a sole intervention to eliminate malaria disease.

In this paper, a mathematical model for the transmission dynamics of Fasciola hepatica in cattle and snail populations is formulated and analyzed. The snail mortality rate (μs) is the most important factor that indirectly impacts the basic reproduction number (R0). A 50% change, either an increase or decrease, in the snail mortality rate will result in an approximate 50% change in the opposite direction in the value of R0. The model shows a forward bifurcation at R0=1, indicating that the disease dynamics undergo a critical transition at this threshold. This change signifies a transition from a disease-free state to a persistent infection, highlighting the possibility of a continuous disease presence given specific epidemiological conditions. Simulations show that reducing miracidia, metacercariae, and snail populations, improving treatment, and lowering pathogen transfer between cattle and snails significantly decrease disease prevalence in cattle. To control the disease, transmission rates for cattle and snails must be reduced below γc=1.4338×10−7 and γs=1.1473×10−8, respectively. Current treatments are insufficient, and a combination of improved treatments reduced transmission rates, and increased snail mortality is recommended for better disease control.

In this paper, we use the fountain theorems to investigate a class of nonlinear Kirchhoff–Poisson type problem. When the nonlinearity f satisfies the Ambrosetti–Rabinowitz’s 4-superlinearity condition, or under some weaker superlinearity condition, we establish two theorems concerning with the existence of infinitely many solutions.

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.

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.

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.

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.

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.

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 α -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α -Krasnosel’skiĭ mapping associated with b -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b -enriched quasinonexpansive mappings have been proved.

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.