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In this paper, we deal with the uniqueness problem of two non-admissible functions sharing some values and sets in the unit disc, and also investigate the problem on an admissible function and a non-admissible function sharing some values and sets. Some theorems of this paper improve the results given by Fang. In addition, the results in this paper analogous version of the uniqueness theorems of meromorphic functions sharing some sets on the whole complex plane which given by Yi and Cao. [ABSTRACT FROM AUTHOR]

This paper deals with stability of nonlinear differential equations with parameter with periodic perturbation. We determine values of the parameter under which the solutions of the perturbed systems could be uniformly exponentially stable. Sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov-like functions are obtained in the sense that the trajectories converge to a small ball centered at the origin. Moreover, to illustrate the applicability of our result, we study the stabilization problem for a class of control system. [ABSTRACT FROM AUTHOR]

Sometimes, it is not possible to find a general solution for some differential equations using some classical methods, like separation of variables. In such a case, one can try to use theory of tensor product of Banach spaces to find certain solutions, called atomic solution. The aim of this paper is to find atomic solution for conformable non-linear wave equation. [ABSTRACT FROM AUTHOR]

In this paper, we tend to apply the proposed modified Laplace Adomian decomposition method that is the coupling of Laplace transform and Adomian decomposition method. The modified Laplace Adomian decomposition method is applied to solve the Fredholm-Volterra integro-differential equations of the second kind in the space L2[a,b]. The nonlinear term will simply be handled with the help of Adomian polynomials. The Laplace decomposition technique is found to be fast and correct. Several examples are tested and also the results of the study are discussed. The obtained results expressly reveal the complete reliability, efficiency, and accuracy of the proposed algorithmic rule for solving the Fredholm-Volterra integro-differential equations and therefore will be extended to other problems of numerous nature. [ABSTRACT FROM AUTHOR]

In this paper, we study nonlinear differential equations arising from the generating functions of degenerate (h; q)-tangent numbers. We give explicit identities for the degenerate (h; q)-tangent numbers. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the existence of asymptotically almost automorphic mild solution to some classes of second order semilinear evolution equation via the techniques of measure of noncompactness. The investigation is based on a new fixed point result which is a generalization of the well known Darbo's fixed point theorem. Finally examples are given to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of truncated exponential polynomials. We give explicit identities for the truncated polynomials. Using numerical investigation, we observe the behavior of complex roots of the truncated polynomials en(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the truncated polynomials en(x). [ABSTRACT FROM AUTHOR]

Besides the feedforward neural networks, there are the recurrent net-works, where the impulses can be transmitted in both directions due to some reaction connections in these networks. Recurrent neural networks are linear or nonlinear dynamic systems. The dynamic behavior presented by the recurrent neural networks can be described both in continuous time, by differential equations and at discrete times by the recurrence relations (difference equations). The distinction between recurrent (or dynamic) neural networks and static neural networks is due to recurrent connec-tions both between the layers of neurons of these networks and within the same layer, too. The aim of this paper is to describe a Recurrent Fuzzy Neural Network (RFNN) model, whose learning algorithm is based on the Improved Particle Swarm Optimization (IPSO) method. Each particle (candidate solution), which is moving permanently includes the parame-ters of the membership function and the weights of the recurrent neural-fuzzy network; initially, their values are randomly generated. The RFNN presented in this paper is unlike the others variants of RFNN models, by the number of the evolution directions that they use: in this paper, we up-date the velocity and the position of all particles along three dimensions, while in [8] are used two dimensions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove some Δ-convergence theorems of iteration processes with errors to approximating a common fixed point for four total asymptotically nonexpansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we solve the inhomogeneous Gauss differential equation and apply this result to estimate the error bound occurring when an analytic function is approximated by an appropriate hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper, we are going to study the Mittag-Leffer-Hyers-Ulam stability and Mittag-Leffer-Hyers-Ulam-Rassias stability of the general Linear Differential Equations of Higher order with constant coefficients using Fourier Transforms method. Moreover, the Mittag-Leffer-Hyers-Ulam stability constants of these differential equations are obtained. Some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper the author derives several interesting differential subordination results. These subordinations are established by means of a differential operator obtained using Ruscheweyh derivative Rm f(z) and the multiplier transformations I (m, λ, l) f(z) namely RImα, λ, l the operator given by RImα : An → An, RImα, λ, l f(z) = (1 - α) Rmf(z) + αI (m, λ, l) f(z), for z ∈ U, m ∈ ℝ, λ, l > 0 and An = {f ∈ H(U) : f(z) = z + an+1 + ..., z ∈ U}, A number of interesting consequences of some of these subordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of the r-Bell polynomials. We give explicit identities for the r-Bell polynomials. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear di¤erence equation... where the parameters α,β,γ, a; b; c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l,k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonstandard finite difference (NSFD) scheme to solve numerically a cholera epidemic model with spatial diffusion. Through constructing discrete Lyapunov functions, we prove the globally asymptotical stabilities of the diseasefree equilibrium and the chronic infection equilibrium, which coincide with the corresponding continuous model. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The object of the present paper is to obtain subordination, superordination and sandwich-type results related to a certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also we point out relevant connections of the results presented here with those obtained in earlier. [ABSTRACT FROM AUTHOR]

By applying Krasnoselskii's and O'Regan's fixed point theorems, in this paper, we study the existence of solutions for a coupled system consisting from Langevin fractional differential equations of Riemann-Liouville type subject to the generalized nonlocal integral boundary conditions. Examples illustrating our results are also presented. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider three types of functions given by sums of products of higher-order Euler functions and derive their Fourier series expansions. Moreover, we express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

This paper aims to study the existence of the solutions for an Impulsive Sequential Fractional Differential Equations of order 1 < q ≤ 2 involving separate boundary conditions. Our analysis relies on some fixed point theorems. In addition, an example is provided to illustrate the results of this study. [ABSTRACT FROM AUTHOR]

In this paper, we investigate systems of nonhomogeneous coupled linear matrix differential equations. Applying Kronecker products, the vector operator, and matrix convolution product, we obtain explicit formula of the general solution to this system in terms of matrix series concerning exponentials and Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two zn+1=zn+tn-l/±tn±tn-1,tn+1=tnzn-l/±zn±zn-l where the initial conditions z-1, z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the dynamics of a system of fourth-order rational difference equations xn+1=xn-3-yn-1/A+xn-3yn-1,yn+1=yn-3-xn-1/A+yn-3xn-1, n=0,1,..., where the parameter A is arbitrary positive real number and the initial conditions x-3,x-2,x-1,x0,y-3,y-2,y-1,y0 are arbitrary nonnegative real numbers. By using new iteration method for the more general nonlinear difference equations and inequality skills, we establish some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for this nonlinear system. Numerical examples to the difference system are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the authors investigate the growth and zeros of the solutions and the coefficients of higher order linear differential equations with entire coefficients of [p, q] - φ order, where p, q are positive integers and satisfy p ≥ q ≥ 1. The theorems that we obtain extend and improve many previous results. [ABSTRACT FROM AUTHOR]

In this paper, a Noval chaotic dynamical system is proposed and the basic properties of the system are investigated. Linear feedback control technique is used to suppress chaos. The controlled system is stable under some conditions on the parameters of the system determined by Lyapunov direct method. In addition, a function projective synchronization of two identical Noval system is presented. Lyapunov method of stability is used to prove the asymptotic stability of solutions for the error dynamical system. Numerical simulations results are included to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-l + b + cxn-k/dxn-s + exn-t, n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants:Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of p-mean piecewise pseudo almost periodic for a stochastic process and establish a new composition theorem about pseudo almost periodic functions under non-Lipschitz-conditions. Using this composition theorem, the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we also study the existence and the global attractiveness for p-mean piecewise pseudo almost periodic mild solutions for impulsive partial neutral stochastic neutral functional diffrential equations. Moreover, an example is given to illustrate the general theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study the impulsive periodic solutions of second order singular ordinary differential equations. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of generalized degenerate tangent polynomials. We give explicit identities for the generalized degenerate tangent polynomials arising from differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

In this paper, some qualitative properties are discussed such as the boundedness, the periodicity and the global stability of the positive solutions of the nonlinear difference equation... where the coefficients A; αi; βi 2 (0,1), i = 1,...., 5; while the initial conditions y-5,y-4,y-3,y-2; y-1; y0 are arbitrary positive real numbers. Some numerical examples will be given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equations f (x+y/2 + z + w) = 1/2 f(x) + 1/2 f(y) + f(z) + f(w), f (x+y+z/3 + w) = 1/3 f(x) + 1/3 f(y) + 1/3 f(z) + f(w) in paranormed spaces. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the one of the orthogonal polynomial namely Generalized Meixner-Pollaczek polynomials, and satisfying subordinate conditions. Taylor-MacLaurin coefficients |α2| and |α3| were estimated for functions in new subclass. Furthermore, several known consequences are also investigated. [ABSTRACT FROM AUTHOR]

In this paper, in order to solve a class of nonlinear bilevel programming problems, we equivalently transform the nonlinear bilevel programming problems into corresponding single level nonlinear programming problems by using the Karush-Kuhn-Tucker optimality condition. Then, based on penalty function theory, we construct a smooth approximation method for obtaining optimal solutions of classic l1-exact penalty function optimality problems, which is equivalent to the single level nonlinear programming problems. Furthermore, using ∈-approximate optimal solution theory, we prove convergence of a simple ∈-approximate optimal algorithm. Finally, through adding parameters in the constraint set of objective function, we prove some perturbation convergence results for solving the nonlinear bilevel programming problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider three types of functions related to higher-order Genocchi functions and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By using Krasnoselskii's fixed point theorem, some sufficient conditions for the existence of positive solutions and the eigenvalue intervals on which there exists a positive solution are obtained. In addition, two examples are presented to demonstrate the application of our main results. [ABSTRACT FROM AUTHOR]

In the present paper, we find the general solution of the inhomogeneous Euler-Cauchy dynamic equation ... on the time scale with the constant graininess function and the linear variable graininess function, respectively. And then, we study the Ulam stability problem of the forgoing equation on different types of time scales. Our results can be viewed as a unfication and extension of the results of Mortici et al. [C. Mortici, T.M. Rassias, S.M. Jung, The inhomogeneous Euler equation and its Hyers-Ulam stability, Appl. Math. Lett. 40 (2015) 23-28]. [ABSTRACT FROM AUTHOR]

In this paper we derive the famous Fekete-Szegö inequality for the class of p-valent non-bazilevič function using differential operator. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear difference equationxn+1 = βxn+βxn-l+γxn-k + axnxn-k/bxn + cxn-l + dxn-k, n = 0, 1, ..., where the parameters α, β, γ, a, b, c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l, k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

This paper studies the existence of extremal solutions for nonlinear fractional differential coupled systems with p-Laplacian operator. The monotone iterative method combined with lower and upper solutions is applied. As an application, an example is presented to illus- trate the main result. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the local stability of the equilibrium points, global attractor, boundedness and the form of the solutions for the following equations xn+1 = Axnxn-3/Bxn + Cxn-2 and xn+1 =Axnxn-3/ Bxn - Cxn-2 , where the coefficients A, B and C are real positive numbers, and the initial conditions x-3,x-2, x-1, x0 are arbitrary non zero real numbers. [ABSTRACT FROM AUTHOR]

This paper proposes a latent Chikungunya viral infection model with saturated incidence rate. To take into account the time lag between the initial viral contacts uninfected monocytes and the production of new active CHIKV particles the model is incorporated by intracellular discrete or distributed time delays. We study the qualitative behavior of the model. Using the method of Lyapunov function, we established the global stability of the steady states of the model. The effect of the time delay on the stability of the steady states has also been shown by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider three types of functions given by the sums of products of poly-Genocchi and poly-Bernoulli functions and derive their Fourier series expansions. Moreover, we will express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

One purpose of this paper is to investigate the growth of analytic function represented by Laplace-Stieltjes transform which is of infinite order and converges in the half plane, and a necessary and sufficient conditions on the growth of Laplace-Stieltjes transforms of finite XU-order was obtained. Besiders, we further investigate the error in approximating on Laplace-Stieltjes transform of finite XU-order, and obtained some relations between the error and growth of Laplace-Stieltjes transforms of finite XU-order. [ABSTRACT FROM AUTHOR]

In this paper, we establish the maximal regularity for the nonlinear functional differential equations with time delay and establish a variation of constant formula for solutions of the given equations. We make use of the regularity of the linear differential equations that appears on given Gelfand triple spaces. [ABSTRACT FROM AUTHOR]

In this paper, we give some necessary conditions on the existence of meromorphic solutions on Fermat type difference equations. We also consider the properties of transcendental entire solutions on the systems of Fermat type differential-difference equations. [ABSTRACT FROM AUTHOR]

In this paper, we will study three types of sums of products of ordered Bell and Genocchi functions and derive their Fourier series expansions. Further, we will express those functions in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRm,nλ,l defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative Rn, given by IRm,n λ,l : A → A, IRm,n λ,l f (z) = (I (m, λ, l) * Rn) f (z) and An = {f ∊ H(U) : f (z) = z + an+1zn+1 + ..., z ∊ U} is the class of normalized analytic functions with A1 = A. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRm,n λ,l and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the linear autonomous system of neutral delay diffierential equations with Riemann-Liouville fractional derivative... where Dαx(t) = [Dαx1(t);Dα2x2(t); ...Dαmxm(t)]T is Riemann-Liouville fractional derivative, the coefficients Pj(j =α; 2...l) and Qi(i =α; 2...n) are real m × m matrices and the delays j(j =α; 2 ...l) and #949;i(i α; 2 ...n) are non-negative real numbers. Sufficient conditions for all solutions of the given equation to be oscillatory are obtained by using fractional calculus and Laplace transform. [ABSTRACT FROM AUTHOR]