Search

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 1. [ABSTRACT FROM AUTHOR]

Nirenberg proposed a problem as to whether or not a continuous and expansive operator T : X ⟶ X (where X is a Hilbert space) is surjective if R T ∘ ≠ ∅. I shall give a positive answer for the problem provided that R T ∘ is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years. [ABSTRACT FROM AUTHOR]

In this paper, we study the hyperstability problem for the well-known σ -Jensen's functional equation f x y + f x σ y = 2 f x for all x , y ∈ S , where S is a semigroup and σ is an involution of S. We present sufficient conditions on E ⊂ ℝ + S 2 so that the inhomogeneous form of σ -Jensen's functional equation f x y + f x σ y = 2 f x + φ x , y for all x , y ∈ S , where the inhomogeneity φ is given, can be E -hyperstable on S. [ABSTRACT FROM AUTHOR]

Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin's maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin's maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented. [ABSTRACT FROM AUTHOR]

In this paper, we consider an initial value problem for the 2-D compressible Navier-Stokes equations without heat conductivity. We prove the global existence of a strong solution when the initial perturbation is small in H 2 and its L 1 norm is bounded. Moreover, we derive some decay estimate for such a solution. [ABSTRACT FROM AUTHOR]

In this paper, we extend the results obtained by Ezearn on annihilated points for his higher-order nonexpansive mappings to the context of general higher-order nonexpansive mappings. Precisely in his thesis, Ezearn introduced the concept of annihilated points, which extends the notion of fixed points, and it is only meaningful in the context of higher-order nonexpansive mappings and gave some mild conditions when the annihilated points could exist in strictly convex Banach spaces. In the last direction, we also extend Ezearn's result on the approximate fixed point sequence for higher-order nonexpansive mappings to general higher-order nonexpansive mappings. [ABSTRACT FROM AUTHOR]

Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations. [ABSTRACT FROM AUTHOR]

The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard's theorem. [ABSTRACT FROM AUTHOR]

In this paper, we explore a generalised solution of the Cauchy problems for the q -heat and q -wave equations which are generated by Jackson's and the q -Sturm-Liouville operators with respect to t and x , respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the q -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions. [ABSTRACT FROM AUTHOR]

By combining the notions of G -metric space and b -metric space, in this paper, we present coincidence fixed-point theorems for p -hybrid mappings in G b -metric spaces. An example is given to demonstrate the novelty of our main results. Henceforth, the illustrative applications are given by using nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

The paper deals with a coupling algorithm using shape and topological derivatives of a given cost functional and a problem governed by nonstationary Maxwell's equations in 3D. To establish the shape and topological derivatives, an adjoint method is used. For the topological asymptotic expansion, two examples of cost functionals are considered with the perturbation of the electric permittivity and magnetic permeability. We combine the shape derivative and topological one to propose an algorithm. The proposed algorithm allows to insert a small inhomogeneity (electric or magnetic) in a given shape. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, G -convergence and H -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation. [ABSTRACT FROM AUTHOR]

In this paper, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used. [ABSTRACT FROM AUTHOR]

In this paper, by using properties of attractive points, we study an iteration scheme combining simplified Baillon type and Mann type to find a common fixed point of commutative two nonlinear mappings in Hilbert spaces. Then, we apply the obtained results to prove a new weak convergence theorem. [ABSTRACT FROM AUTHOR]

Based on the concept of pseudocomplement, we introduce a new representation of preopenness of L -fuzzy sets in R L -fuzzy bitopological spaces. The concepts of pairwise R L -fuzzy precontinuous and pairwise R L -fuzzy preirresolute functions are extended and discussed based on the i , j - R L -preopen gradation. Further, we follow up with a study of pairwise R L -fuzzy precompactness in R L -fuzzy bitopological spaces of an L -fuzzy set. We find that our paper offers more general results since R L -fuzzy bitopology is a generalization of L -bitopology, R L -bitopology, and L -fuzzy topology. [ABSTRACT FROM AUTHOR]

In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle. [ABSTRACT FROM AUTHOR]

In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations. [ABSTRACT FROM AUTHOR]

In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. We determine the general solution to the symmetric cell division problem for a certain class of coefficients and establish the convergence of solutions to a large time asymptotic solution. The existence of a steady size distribution (SSD) solution for an asymmetric cell division problem is established and is shown to be the large time-attracting solution for a certain class of coefficients. The rate of convergence of solutions towards the SSD solution is affected by the choice of coefficients and remains unaffected by the asymmetry in cell division. The uniqueness of solutions to the initial boundary value problem is also established. [ABSTRACT FROM AUTHOR]

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin's maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem. [ABSTRACT FROM AUTHOR]

It is known that injective (complex or real) W ∗ -algebras with particular factors have been studied well enough. In the arbitrary cases, i.e., in noninjective case, to investigate (up to isomorphism) W ∗ -algebras is hard enough, in particular, there exist continuum pairwise nonisomorphic noninjective factors of type II. Therefore, it seems interesting to study maximal injective W ∗ -subalgebras and subfactors. On the other hand, the study of maximal injective W ∗ -subalgebras and subfactors is also related to the well-known von Neumann's bicommutant theorem. In the complex case, such subalgebras were investigated by S. Popa, L. Ge, R. Kadison, J. Fang, and J. Shen. In recent years, studies have also begun in the real case. Let us briefly recall the relevance of considering the real case. It is known that in the works of D. Topping and E. Stormer, it was shown that the study of JW-algebras (nonassociative real analogues of von Neumann algebras) of types II and III is essentially reduced to the study of real W ∗ -algebras of the corresponding type. It turned out that the structure of real W ∗ -algebras, generally speaking, differs essentially in the complex case. For example, in the finite-dimensional case, in addition to complex and real matrix algebras, quaternions also arise, i.e., matrix algebras over quaternions. In the infinite-dimensional case, it is proved that there exist, up to isomorphism, two real injective factors of type III λ (0 < λ < 1), and a countable number of pairwise nonisomorphic real injective factors of type III 0 , whose enveloping (complex) W ∗ -factors are isomorphic, is constructed. It follows from the above that the study of the real analogue of problems in the theory of operator algebras is topical. Moreover, the real analogue is a generalization of the complex case, since the class of real linear operators is much wider than the class of complex linear operators. In this paper, the maximal injective real W ∗ -subalgebras of real W ∗ -algebras or real factors are investigated. For real factors Q ⊂ R , it is proven that if Q + i Q is a maximal injective W ∗ -subalgebra in R + i R , then Q also is a maximal injective real W ∗ -subalgebra in R. The converse is proved in the case " II 1 "-factors, that is, it is shown that if R is a real factor of type II 1 , then the maximal injectivity of Q implies the maximal injectivity of Q + i Q. Moreover, it is proven that a maximal injective real subfactor Q of a real factor R is a maximal injective real W ∗ -subalgebra in R if and only if Q is irreducible in R , i.e., Q ′ ∩ R = ℝ I where I is the unit. The "splitting theorem" of Ge-Kadison in the real case is also proven, namely, if R 1 is a finite real factor, R 2 is a finite real W ∗ -algebra, and R is a real W ∗ -subalgebra of R 1 ⊗ ¯ R 2 containing R 1 ⊗ ¯ ℝ I , then there is some real W ∗ -subalgebra Q 2 ⊂ R 2 such that R = R 1 ⊗ ¯ Q 2 . Moreover, it is given some affirmative answers to the question of S. Popa for the real case. [ABSTRACT FROM AUTHOR]

This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized α , ψ -contraction mappings in the setting of rectangular b -metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results. [ABSTRACT FROM AUTHOR]

This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in G -metric spaces. Henceforth, results obtained will be verified with the help of illustrative examples. Also, we demonstrate the results with an application. [ABSTRACT FROM AUTHOR]

In this paper, we consider a JS metric space endowed with convexity structure, which will allow us to examine and study convergence of Mann iteration and Ishikawa iteration for Banach type and Chatterjea type contractions defined on JS metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems for k -demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm. [ABSTRACT FROM AUTHOR]

The Bishop frame or rotation minimizing frame (RMF) is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of computer graphics, engineering, and biology. The main aim of this paper is using the RMF for classification of singularity type of timelike sweeping surface and Bishop spherical Darboux image which is mightily concerning a unit speed spacelike curve with timelike binormal vector in E 1 3 . [ABSTRACT FROM AUTHOR]

In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model. [ABSTRACT FROM AUTHOR]

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm. [ABSTRACT FROM AUTHOR]

In this paper, the notion of set-valued L -contractions is introduced, and a new fixed point theorem for such contractions is established. An example to illustrate main theorem is given. [ABSTRACT FROM AUTHOR]

We prove lower semicontinuity in L 1 Ω for a class of functionals G : B V Ω ⟶ ℝ of the form G u = ∫ Ω g x , ∇ u d x + ∫ Ω ψ x d D s u where g : Ω × ℝ N ⟶ ℝ , Ω ⊂ ℝ N is open and bounded, g · , p ∈ L 1 Ω for each p , satisfies the linear growth condition lim p ⟶ ∞ g x , p / p = ψ x ∈ C Ω ∩ L ∞ Ω , and is convex in p depending only on p for a.e. x. Here, we recall for u ∈ B V Ω ; the gradient measure D u = ∇ u d x + d D s u x is decomposed into mutually singular measures ∇ u d x and d D s u x . As an example, we use this to prove that ∫ Ω ψ x α 2 x + ∇ u 2 d x + ∫ Ω ψ x d D s u is lower semicontinuous in L 1 Ω for any bounded continuous ψ and any α ∈ L 1 Ω. Under minor addtional assumptions on g , we then have the existence of minimizers of functionals to variational problems of the form G u + u − u 0 L 1 for the given u 0 ∈ L 1 Ω , due to the compactness of B V Ω in L 1 Ω. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation. [ABSTRACT FROM AUTHOR]

Chaundy and Jolliffe proved that if a n is a nonnegative, nonincreasing real sequence, then series ∑ a n sin n x converges uniformly if and only if n a n ⟶ 0. The purpose of this paper is to show that if n a n is nonincreasing and n a n ⟶ 0 , then the series f x = ∑ a n sin n x can be differentiated term-by-term on c , d for c , d > 0. However, f ′ 0 may not exist. [ABSTRACT FROM AUTHOR]

In this paper, we show that in order for a proper compact subset K of plane ℝ 2 to be convex, it is necessary and sufficient that inverse norm function be subharmonic. [ABSTRACT FROM AUTHOR]

For q > 1, a new Green's function provides solutions of inhomogeneous multiplicatively advanced ordinary differential equations (iMADEs) of form y(N)(t) − Ay(qt) = f(t) 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 f(t) 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 f(t) 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. [ABSTRACT FROM AUTHOR]

In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation's result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method's power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We focus on the global existence and L p − L q rates of convergence for the compressible magnetohydrodynamic equations in R 3 . 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 H 3 . Rates of convergence for the solution in L q norm with 2 ≤ q ≤ 6 and its first- and second-order derivatives in L 2 norm are obtained, if the initial data belong to L p with 1 ≤ p ≤ 6 5. [ABSTRACT FROM AUTHOR]

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of Fuchsian type in time t and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the parameter ϵ known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic-type functions in time and are bounded holomorphic in space. A set of logarithmic-type solutions are shaped by means of Laplace transforms relatively to t and ϵ and Fourier integrals in space. Furthermore, a formal logarithmic-type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to ϵ on bounded sectors at the origin. [ABSTRACT FROM AUTHOR]