Abstract: The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results. PubDate: Fri, 20 Jan 2023 13:35:02 +000
Abstract: In this paper, we explore a generalised solution of the Cauchy problems for the -heat and -wave equations which are generated by Jackson’s and the -Sturm-Liouville operators with respect to and , 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 -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions. PubDate: Thu, 19 Jan 2023 09:50:02 +000
Abstract: In this article, we mainly discuss the existence and uniqueness of fixed point satisfying integral type contractions in complete metric spaces via rational expression using real-valued functions. We improve and unify many widely known results from the literature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we conclude with an example presented graphically in favour of our work. PubDate: Thu, 05 Jan 2023 12:20:02 +000
Abstract: By combining the notions of -metric space and -metric space, in this paper, we present coincidence fixed-point theorems for -hybrid mappings in -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. PubDate: Thu, 08 Dec 2022 15:50:01 +000
Abstract: In this work, we study the effect of nonlinear source term in Black-Scholes model by finding the solution of it. We use the mathematical concepts of existence and uniqueness to arrive the conclusion. The transformation of the nonlinear equation into heat equation leads to the existence of solution through fixed-point theorems, semigroup theory, and certain regularity conditions imposed on variables. PubDate: Mon, 28 Nov 2022 06:20:01 +000
Abstract: Meningitis is an inflammation of the meninges, which covers the brain and spinal cord. Every year, most individuals within sub-Saharan Africa suffer from meningococcal meningitis. Moreover, tens of thousands of these cases result in death, especially during major epidemics. The transmission dynamics of the disease keep changing, according to health practitioners. The goal of this study is to exploit robust mechanisms to manage and prevent the disease at a minimal cost due to its public health implications. A significant concern found to aid in the transmission of meningitis disease is the movement and interaction of individuals from low-risk to high-risk zones during the outbreak season. Thus, this article develops a mathematical model that ascertains the dynamics involved in meningitis transmissions by partitioning individuals into low- and high-risk susceptible groups. After computing the basic reproduction number, the model is shown to exhibit a unique local asymptotically stability at the meningitis-free equilibrium , when the effective reproduction number , and the existence of two endemic equilibria for which and exhibits the phenomenon of backward bifurcation, which shows the difficulty of relying only on the reproduction number to control the disease. The effective reproductive number estimated in real time using the exponential growth method affirmed that the number of secondary meningitis infections will continue to increase without any intervention or policies. To find the best strategy for minimizing the number of carriers and infected individuals, we reformulated the model into an optimal control model using Pontryagin’s maximum principles with intervention measures such as vaccination, treatment, and personal protection. Although Ghana’s most preferred meningitis intervention method is via treatment, the model’s simulations demonstrated that the best strategy to control meningitis is to combine vaccination with treatment. But the cost-effectiveness analysis results show that vaccination and treatment are among the most expensive measures to implement. For that reason, personal protection which is the most cost-effective measure needs to be encouraged, especially among individuals migrating from low- to high-risk meningitis belts. PubDate: Mon, 21 Nov 2022 11:50:01 +000
Abstract: 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. PubDate: Fri, 18 Nov 2022 08:05:05 +000
Abstract: In this work, we shall derive a new subclass of univalent analytic functions denoted by in the open unit disk which is defined by multiplier transformation. Coefficient inequalities, growth and distortion theorem, extreme points, and radius of starlikeness and convexity of functions belonging to the subclass are obtained. PubDate: Wed, 05 Oct 2022 11:05:01 +000
Abstract: In the present study, the effect of thermal stratification and heat generation in the boundary layer flow of the Eyring-Powell fluid over the stratified extending surface due to convection has been investigated. The governing equations of the flow are transformed from partial differential equations into a couple of nonlinear ordinary differential equations via similarity variables. The optimal homotopy asymptotic method (OHAM) is used to acquire the approximate analytical solution to the problems. Impacts of flow regulatory parameters on temperature, velocity, skin friction coefficient, and Nusselt number are examined. It is discovered that the fluid velocity augments with a greater value of material parameter , mixed convection parameter , and material fluid parameter . The result also revealed that with a higher value of the Prandtl number Pr and the stratified parameter , the temperature and the velocity profile decreases, but the opposite behavior is observed when the heat generation/absorption parameter increases. The results are compared with available literature and are in good harmony. The present study has substantial ramifications in industrial, engineering, and technological applications, for instance, in designing various chemical processing equipment, distribution of temperature and moisture over agricultural fields, groves of fruit trees, environmental pollution, geothermal reservoirs, thermal insulation, enhanced oil recovery, and underground energy transport. PubDate: Fri, 23 Sep 2022 08:35:00 +000
Abstract: In this article, we define the new generalized Hahn sequence space , where is monotonically increasing sequence with for all , and . Then, we prove some topological properties and calculate the ,, and duals of . Furthermore, we characterize the new matrix classes , where , and , where . In the last section, we prove the necessary and sufficient conditions of the matrix transformations from into , and from into . PubDate: Fri, 16 Sep 2022 10:35:02 +000
Abstract: 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, -convergence and -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation. PubDate: Wed, 31 Aug 2022 15:20:02 +000
Abstract: 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. PubDate: Fri, 26 Aug 2022 11:35:00 +000
Abstract: 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. PubDate: Wed, 24 Aug 2022 10:50:03 +000
Abstract: 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. PubDate: Mon, 08 Aug 2022 11:05:02 +000
Abstract: We examine a family of nonlinear difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation difference operators, recently investigated by the author, and quasilinear Kowalevski type problems that involve contraction difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and Gevrey structure are exhibited. The other feature concerns the problem of confluence of these solutions as tends to 1. PubDate: Mon, 08 Aug 2022 06:35:02 +000
Abstract: 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. PubDate: Thu, 28 Jul 2022 10:20:01 +000
Abstract: The primary aim of this work is to introduce a new class of functions called --pseudo-almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those --pseudo-almost periodic functions including two new composition results which play a crucial role for the existence of some --pseudo-almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the --pseudo-almost periodic solutions for some models of Lasota-Wazewska equation with measure -pseudo-almost periodic coefficient and mixed delays. PubDate: Tue, 26 Jul 2022 11:35:01 +000
Abstract: Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. In this work, therefore, the authors defined a univalent function associated with the beta function with . Some geometric properties of the function are discussed. PubDate: Mon, 25 Jul 2022 11:35:03 +000
Abstract: In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in 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. PubDate: Mon, 11 Jul 2022 11:05:03 +000
Abstract: For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this set of relations, the current study forges a systematic connection between the theory of MADEs and that of special functions. In a large subset of the general case, we introduce a new family of Schwartz wavelet MADE solutions for and rational with . These have all moments vanishing and have a Fourier transform related to theta functions. For low parameter values derived from , the connection of the to the theory of wavelet frames is begun. For a second set of low parameter values derived from , the notion of a canonical extension is introduced. A number of examples are discussed. The study of convergence of the MADE solution to the solution of its analogous ODE is begun via an in depth analysis of a normalized example . A useful set of generalized -Wallis formulas are developed that play a key role in this study of convergence. PubDate: Thu, 07 Jul 2022 10:05:03 +000
Abstract: In this article, we study and investigate the analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact solutions of the fractional mKDV-ZK equation by using first integral method; we found new types of hyperbolic solutions and trigonometric solutions by symbolic computation. PubDate: Mon, 20 Jun 2022 11:20:01 +000
Abstract: The estimates were obtained for the number of solutions for the Neumann and Dirichlet boundary value problems associated with the Liénard equation with a quadratic dependence on the “velocity.” Sabatini’s transformation is used to reduce this equation to a conservative one, which does not contain the derivative of an unknown function. Despite the one-to-one correspondence between the equilibria, the topological structure of the phase portraits of both equations can differ significantly. PubDate: Sat, 11 Jun 2022 07:35:03 +000
Abstract: 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. PubDate: Mon, 06 Jun 2022 08:20:01 +000
Abstract: Regarding the concept of size function topology, this allows us to view the topological space as a metric-like space. We prove the existence and uniqueness for a coupled fixed point of the map satisfying some certain contractive conditions. PubDate: Fri, 03 Jun 2022 04:35:02 +000
Abstract: 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. PubDate: Sat, 28 May 2022 04:50:01 +000
Abstract: A two-generator Kleinian group can be naturally associated with a discrete group with the generator of order two and where This is useful in studying the geometry of the Kleinian groups since will be discrete only if is, and the moduli space of groups is one complex dimension less. This gives a necessary condition in a simpler space to determine the discreteness of . The dimension reduction here is realised by a projection of principal characters of the two-generator Kleinian groups. In applications, it is important to know that the image of the moduli space of Kleinian groups under this projection is closed and, among other results, we show how this follows from Jørgensen’s results on algebraic convergence. PubDate: Fri, 06 May 2022 12:20:01 +000
Abstract: 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 (), and a countable number of pairwise nonisomorphic real injective factors of type , 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 , it is proven that if is a maximal injective W-subalgebra in , then also is a maximal injective real W-subalgebra in . The converse is proved in the case “”-factors, that is, it is shown that if is a real factor of type , then the maximal injectivity of implies the maximal injectivity of . Moreover, it is proven that a maximal injective real subfactor of a real factor is a maximal injective real W-subalgebra in if and only if is irreducible in , i.e., where is the unit. The “splitting theorem” of Ge-Kadison in the real case is also proven, namely, if is a finite real factor, is a finite real W-algebra, and is a real W-subalgebra of containing , then there is some real W-subalgebra such that . Moreover, it is given some affirmative answers to the question of S. Popa for the real case. PubDate: Mon, 25 Apr 2022 12:20:07 +000
Abstract: 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. PubDate: Tue, 12 Apr 2022 06:50:01 +000
Abstract: The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation. PubDate: Tue, 05 Apr 2022 14:50:00 +000
Abstract: In this paper, we introduce generalized -contraction mappings in the setting of rectangular -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. PubDate: Tue, 05 Apr 2022 08:50:02 +000
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