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The present article aims to determine the green economic policies of an inventory model for non-instantaneous deteriorating items under practical scenarios. These scenarios involve specific maximum lifetimes for items with deteriorations controllable through investments in preservation technologies, which can affect the period without deterioration. Additionally, carbon is emitted due to energy-related costs, prompting retailers to invest in green technology investments to reduce carbon emissions concurrently under the carbon tax policy and the carbon cap-and-trade policy simultaneously. Meanwhile, when a retailer is required to make a prepayment, the purchase discount policy is contingent on the number of installments offered. This means that the retailer prepays off the entire purchasing cost with a single installment, thereby receiving a maximum percentage of price discount. Otherwise, the retailer prepays a certain fraction of the purchasing cost with multiple installments, and the percentage of the price discount will be contingent on the number of n identical installments. In this context, we present theoretical results for optimal solutions, and a salient algorithm is presented, which is derived from these theoretical findings within a sustainable inventory system. To better illustrate the proposed mathematical problems, several numerical examples are presented, followed by sensitivity analysis for different scenarios. [ABSTRACT FROM AUTHOR]

This article deals with a free boundary problem of the Lotka-Volterra type prey-predator model with advection in one space dimension. The model considered here may be applied to describe the expanding of an invasive or new predator species adopting a combination of random movement and advection upward or downward along the resource gradient, with the free boundaries representing expanding fronts of predator species. The main purpose of this article is to understand the influence of the advection environment on the dynamics of the model. We provide sufficient conditions for spreading and vanishing of the predator species, and we find a sharp threshold between the spreading and vanishing concerning this model. Moreover, for the case of successful spreading for the predator, we give estimates of asymptotic spreading speeds and nonlocal long-time behavior of the prey and the predator. [ABSTRACT FROM AUTHOR]

In the present paper, we give the bounds for the second Hankel determinant of the logarithmic coefficients of a certain subclass of normalized univalent functions, which we have introduced here. Relevant connections of the results, which we have presented here, with those available in the existing literature are also described briefly [ABSTRACT FROM AUTHOR]

A spectral collocation-based approximate algorithm is adapted for the numerical evaluation of a class of fractional-order delay differential equations. The involved fractional operators are defined as the Caputo-Fabrizio and Liouville-Caputo derivatives. A novel family of polynomials called Narayana polynomials and their generalization forms are utilized in our collocation procedure. We study the convergent analysis of the Narayana polynomials in a weighted L2 norm and obtain an upper bound for their series expansion form. The performance of the present matrix collocation is justified by solving three test examples using both fractional operators and various fractional orders. The outcomes are compared with two existing numerical approaches, i.e., the modified operational matrix method (MOMM) and the operational matrix of integration relied on Taylor bases (OMTB). A comparison study reveals that our results are more accurate than these two methods and thus the presented matrix algorithm is superior in terms of efficacy and applicability. [ABSTRACT FROM AUTHOR]

In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass ΓΣ(δ, ρ, τ, η, φ) of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained. [ABSTRACT FROM AUTHOR]

This paper focuses on a chemotaxis model with no-flux boundary conditions. We first discuss the stability of the unique positive equilibrium by treating the chemotaxis coefficient \xi as the Hopf bifurcation and the steady state bifurcation parameter. Hereafter, we perform the existence and stability of the bifurcating solution, which bifurcated from the steady state bifurcation, by using the Crandall-Rabinowitz local bifurcation theory. It is noticed that few existing literatures give a discriminant to determine the stability of the bifurcating solution for the chemotaxis models. To this end, we will fill this gap, and an explicit formula will be presented. This technique can also be applied in other ecological models with chemotaxis. [ABSTRACT FROM AUTHOR]

In this paper, we expose the ideas of point-wise statistical convergence, equi-statistical convergence and uniform statistical convergence in the sense of the deferred power-series method. We then propose a relation connecting them, which is followed by several illustrative examples. Moreover, as an application viewpoint, we establish an approximation theorem based upon our proposed method for equi-statistical convergence of sequences of positive linear operators. Finally, we estimate the equi-statistical rates of convergence for the effectiveness of the results presented in our study. [ABSTRACT FROM AUTHOR]

In this article, the authors propose to investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg–De Vries equation involving many different kernels. In order to transform these models into a set or system of differential equations, various properties of the first-kind Chebyshev polynomial are used in this study. The main objective of the present study is to apply the spectral collocation approach for the multi-space fractional-order coupled Korteweg–De Vries equation with different kernels. We use finite differences to numerically solve these differential equations by reducing them to algebraic equations. The Newton (or, more precisely, the Newton–Raphson) method is then used to solve these resulting algebraic equations. By calculating the error involved in our approach, the precision of the numerical solution is verified. The use of spectral methods, which provide excellent accuracy and exponential convergence for issues with smooth solutions, is shown to be a benefit of the current study. [ABSTRACT FROM AUTHOR]

Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular singularly-perturbed boundary and initial value problems are presented using a novel quintic B-spline (QBS) approximation approach. This method uses a quasi-linearization approach to solve SSPNL initial/boundary value problems. And the non-linear problems are transformed into a sequence of linear problems by applying the quasi-linearization approach. The QBS functions produce more accurate results when compared to other existing approaches because of their local support, symmetry, and partition of unity features. This method can be applied to immediately solve the SSPPs without reducing the order in which they are presented. It has been demonstrated that the suggested numerical approach converges uniformly over the whole domain. The proposed approach is implemented on a few problems to validate the scheme. The computational results are compared, and they illustrate that the proposed approach performs better. [ABSTRACT FROM AUTHOR]

This paper presents a new general subfamily N Σ m u , v (η , μ , γ , ℓ) of the family Σ m that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk D associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients a m + 1 and a 2 m + 1 , and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results. [ABSTRACT FROM AUTHOR]

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R ℘ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symmetry is crucial. It provides insightful explanations, clearer explanations, and useful methods to help with the learning of key mathematical ideas. The kernel of the general family of weighted fractional integral operators is related to a wide variety of extensions and generalizations of the Mittag-Leffler function and the Hurwitz-Lerch zeta function. It delves into the applications of fractional-order integral and derivative operators in mathematical and engineering sciences. Furthermore, this article derives specific cases for selected functions and presents various applications to illustrate the obtained results. Additionally, novel applications involving the Digamma function are introduced. [ABSTRACT FROM AUTHOR]

We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic financial system numerically, we use the generalized version of modified Bessel polynomials (GMBPs) in the collocation matrix approaches along with the domain-splitting strategy. Whereas the first matrix collocation scheme is directly applied to the financial model problem, the second one is a combination of the quasilinearization method and the direct first numerical matrix method. In the former approach, we arrive at nonlinear algebraic matrix equations while the resulting systems are linear in the latter method and can be solved more efficiently. A convergence theorem related to GMBPs is proved and an upper bound for the error is derived. Several simulation outcomes are provided to show the utility and applicability of the presented matrix collocation procedures. [ABSTRACT FROM AUTHOR]

By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A , where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article. [ABSTRACT FROM AUTHOR]

Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra–Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach. [ABSTRACT FROM AUTHOR]

This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable conditions are developed to prove the proposed model's continues behavior which reflects the stable generation. At last, three test examples are presented to verify the established theoretical concepts. [ABSTRACT FROM AUTHOR]

In this paper, we obtain degree of convergence of a function of two‐dimensional variables in generalized Hölder spaces by matrix means of its conjugate Fourier series. We also obtain degree of convergence of a function of N‐dimensional variables in generalized Hölder spaces by matrix means of its conjugate Fourier series. We also deduce important corollaries from our main results. [ABSTRACT FROM AUTHOR]

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α , strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three. [ABSTRACT FROM AUTHOR]