Articles

Existence solutions for boundary value problem of nonlinear fractional q-difference equations

In this paper, we discuss the existence of weak solutions for a nonlinear boundary value problem of fractional q-difference equations in Banach space. Our analysis relies on the Mönch’s fixed-point theorem combin...

Authors: Wen-Xue Zhou and Hai-Zhong Liu

Oscillation criteria for second-order nonlinear neutral dynamic equations with distributed deviating arguments on time scales

In this article, we establish some new oscillation criteria and give sufficient conditions to ensure that all solutions of nonlinear neutral dynamic equation of the form

Authors: Tuncay Candan

On ℐ-asymptotically lacunary statistical equivalent sequences

This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, ℐ-statistically limit and ℐ-lacunary statistical convergence. Let θ be a lacunary seq...

Authors: Ekrem Savaş

On zeros of the characteristic determinant of the spectral problem for a third-order differential operator on a segment with nonlocal boundary conditions

In the paper, we consider distribution of eigenvalues of a third-order differential operator with nonlocal boundary conditions on a segment. The characteristic operator of the considered spectral problem is an...

Authors: Nurlan S Imanbaev, Baltabek E Kanguzhin and Burkhan T Kalimbetov

Regularized asymptotical solutions of integro-differential systems with spectral singularities

In the work, the Cauchy problem is considered for a singularly perturbed system with zero points of the spectrum. It is proved normal solvability of general iterative problems. Unique solvability and convergen...

Authors: Burkhan Kalimbetov, Lesbek Tashimov, Nurlan Imanbaev and Dinmukhambet Sapakov

On a class of q-Bernoulli and q-Euler polynomials

The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q

Authors: Nazim I Mahmudov

Differential equations for the extended 2D Bernoulli and Euler polynomials

In this paper, we introduce the extended 2D Bernoulli polynomials by

Authors: Banu Yılmaz and Mehmet Ali Özarslan

Solutions for a class of nonlinear Volterra integral and integro-differential equation using cyclic $(\phi ,\psi ,\theta )$-contraction

We establish the existence and uniqueness of solutions for a class of nonlinear Volterra integral and integro-differential equations using fixed-point theorems for a new variant of cyclic ...

Authors: Hemant Kumar Nashine, RP Pathak, Piyusha S Somvanshi, Slavisa Pantelic and Poom Kumam

Some subordination results associated with generalized Srivastava-Attiya operator

Authors: Adel A Attiya and Ali H Hakami

A Jacobi operational matrix for solving a fuzzy linear fractional differential equation

This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order ...

Authors: Ali Ahmadian, Mohamed Suleiman, Soheil Salahshour and Dumitru Baleanu

Higher-order Bernoulli, Euler and Hermite polynomials

In (Kim and Kim in J. Inequal. Appl. 2013:111, 2013; Kim and Kim in Integral Transforms Spec. Funct., 2013, doi:10.1080/10652469.2012.754756), we have investigated some properties of higher-order Bernoulli and...

Authors: Dae San Kim, Taekyun Kim, Dmitry V Dolgy and Seog-Hoon Rim

Nonstandard finite difference schemes for a fractional-order Brusselator system

In this paper, we discuss numerical methods for fractional order problems. Some nonstandard finite difference schemes are presented and investigated. The application in the simulation of a fractional-order Bru...

Authors: Mevlüde Yakıt Ongun, Damla Arslan and Roberto Garrappa

Properties of convolutions for hypergeometric series with univalent functions

The purpose of the present paper is to investigate various mapping and inclusion properties involving subclasses of analytic and univalent functions for a linear operator defined by means of Hadamard product (...

Authors: Ji A Kim and Nak Eun Cho

Birth, growth and computation of pi to ten trillion digits

The universal real constant pi, the ratio of the circumference of any circle and its diameter, has no exact numerical representation in a finite number of digits in any number/radix system. It has conjured up ...

Authors: Ravi P Agarwal, Hans Agarwal and Syamal K Sen

Chaotic behavior in a class of delay difference equations

In this paper, we rigorously prove the existence of chaos in a class of delay difference equations, which can be viewed as a discrete analogue of a one-dimensional delay differential equation by using the Eule...

Authors: Zongcheng Li, Qingli Zhao and Di Liang

Value distribution of difference and q-difference polynomials

In this paper, we investigate the value distribution of difference polynomial and obtain the following result, which improves a recent result of K. Liu and L.Z. Yang: Let f be a transcendental meromorphic functio...

Authors: Nan Li and Lianzhong Yang

Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator

This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equat...

Authors: Wei-Hua Su, Xiao-Jun Yang, H Jafari and Dumitru Baleanu

Extended p-adic q-invariant integrals on ${\mathbb{Z}}_p$ associated with applications of umbral calculus

The fundamental aim of this paper is to consider some applications of umbral calculus by utilizing from the extended p-adic q-invariant integral on

Authors: Serkan Araci, Mehmet Acikgoz and Adem Kilicman

Dynamics of a discrete Lotka-Volterra model

In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by

Authors: Qamar Din

Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4⁺ cells and attractor one-dimensional Keller-Segel equations

In this paper, we make use of the relatively new analytical technique, the homotopy decomposition method (HDM), to solve a system of fractional nonlinear differential equations that arise in the model for HIV ...

Authors: Abdon Atangana and Ernestine Alabaraoye

Subordination properties for a general class of integral operators involving meromorphically multivalent functions

The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain nonlinear integral operators defined on the space of meromorphically p-valent functions ...

Authors: Nak Eun Cho and Rekha Srivastava

Asymptotically polynomial solutions of difference equations

Asymptotic properties of solutions of a difference equation of the form

Authors: Janusz Migda

An application of measures of noncompactness in the investigation of boundedness of solutions of second-order neutral difference equations

The purpose of this paper is to investigate a nonlinear second-order neutral difference equation of the form

Authors: Ewa Schmeidel

On the value distribution and uniqueness of difference polynomials of meromorphic functions

In this paper, we study the zeros of difference polynomials of meromorphic functions of the forms

Authors: Hong-Yan Xu

On certain univalent functions with missing coefficients

The main object of the present paper is to show certain sufficient conditions for univalency of analytic functions with missing coefficients.

Authors: Yi-Ling Cang and Jin-Lin Liu

Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument

By using Mawhin’s continuation theorem in the coincidence degree theory, some criteria for guaranteeing the existence of periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argu...

Authors: Jin Li, Jianlin Luo and Yun Cai

Dynamical behaviors of a discrete SIS epidemic model with standard incidence and stage structure

A discrete SIS epidemic model with stage structure and standard incident rate which is governed by Beverton-Holt type is studied. The sufficient conditions on the permanence and extinction of disease are estab...

Authors: Zhidong Teng, Linfei Nie and Jiabo Xu

Robust $H_{\mathrm{\infty }}$ control of switched stochastic systems with time delays under asynchronous switching

Authors: Guoxin Chen and Zhengrong Xiang

Symplectic difference systems with periodic coefficients: Krein’s traffic rules for multipliers

We investigate symplectic difference systems with periodic coefficients. We show that the known traffic rules for eigenvalues of the monodromy matrix of linear Hamiltonian differential and difference systems c...

Authors: Ondřej Došlý

Eisenstein series and their applications to some arithmetic identities and congruences

Authors: Daeyeoul Kim, Aeran Kim and Ayyadurai Sankaranarayanan

On a nonlinear fractional differential equation on partially ordered metric spaces

In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation ...

Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

Positive solutions of second-order linear difference equation with variable delays

In this paper we consider the second-order linear difference equations with variable delays

Authors: Hajnalka Peics

Two-parameter Srivastava polynomials and several series identities

In the present paper, we introduce two-parameter Srivastava polynomials in one, two and three variables by inserting new indices, where in the special cases they reduce to (among others) Laguerre, Jacobi, Bess...

Authors: Cem Kaanoglu and Mehmet Ali Özarslan

Stability and convergence of the space fractional variable-order Schrödinger equation

The space fractional Schrödinger equation was further extended to the concept of space fractional variable-order derivative. The generalized equation is very difficult to handle analytically. We solved the gen...

Authors: Abdon Atangana and Alain H Cloot

Stability analysis of a host parasite model

Host parasite models are similar to host parasitoid models except that the parasite does not necessarily kill the host. Leslie/Gower model (Leslie and Gower in Biometrika 47(3/4):219-234, 1960) played a histor...

Authors: Ünal Ufuktepe and Sinan Kapçak

Separated boundary value problem for fractional differential equations depending on lower-order derivative

We study a new class of boundary value problems of nonlinear fractional differential equations whose nonlinear term depends on a lower-order fractional derivative with fractional separated boundary conditions....

Authors: Xiaoyou Liu and Zhenhai Liu

An estimate of Sumudu transforms for Boehmians

The space of Boehmians is constructed using an algebraic approach that utilizes convolution and approximate identities or delta sequences. A proper subspace can be identified with the space of distributions. I...

Authors: Shrideh Khalaf Qasem Al-Omari and Adem Kılıçman

Power series method and approximate linear differential equations of second order

In this paper, we will establish a theory for the power series method that can be applied to various types of linear differential equations of second order to prove the Hyers-Ulam stability.

Authors: Soon-Mo Jung and Hamdullah Şevli

The poles and growth of solutions of systems of complex difference equations

In view of the Nevanlinna theory, we study the growth and poles of solutions of some classes of systems of complex difference equations and obtain some interesting results such as the lower bounds for Nevanlin...

Authors: Hua Wang, Hong-Yan Xu and Bing-Xiang Liu

New identities involving Bernoulli, Euler and Genocchi numbers

Using p-adic integral, many new convolution identities involving Bernoulli, Euler and Genocchi numbers are given.

Authors: Su Hu, Daeyeoul Kim and Min-Soo Kim

Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus

In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of s...

Authors: Dae San Kim, Taekyun Kim, Dmitry V Dolgy and Seog-Hoon Rim

Stability of quadratic functional equations in generalized functions

In this paper, we consider the following generalized quadratic functional equation with n-independent variables in the spaces of generalized functions:

Authors: Young-Su Lee

On the iterated exponent of convergence of zeros of $f^{(j)}(z)-\phi (z)$

Authors: Jin Tu, Zu-Xing Xuan and Hong-Yan Xu

A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations

In this paper, we propose a new three-level implicit nine-point compact finite difference formulation of order two in time and four in space directions, based on spline in tension approximation in x-direction and...

Authors: Ranjan K Mohanty and Venu Gopal

Extension of the differential transformation method to nonlinear differential and integro-differential equations with proportional delays

In this paper, the differential transformation method is applied by providing new theorems to develop exact and approximate solutions of nonlinear differential and integro-differential equations with proportio...

Authors: Zdeněk Šmarda, Josef Diblík and Yasir Khan

Dark soliton and periodic wave solutions of nonlinear evolution equations

This paper studies the Kudryashov-Sinelshchikov and Jimbo-Miwa equations. Subsequently, we formally derive the dark (topological) soliton solutions for these equations. By using the sine-cosine method, some ad...

Authors: Özkan Güner, Ahmet Bekir and Adem Cengiz Cevikel

Chain components with $C^1$-stably orbital shadowing

Authors: Manseob Lee

Statistical convergence through de la Vallée-Poussin mean in locally solid Riesz spaces

The notion of statistical convergence was defined by Fast (Colloq. Math. 2:241-244, 1951) and over the years was further studied by many authors in different setups. In this paper, we define and study statisti...

Authors: Syed Abdul Mohiuddine, Abdullah Alotaibi and Mohammad Mursaleen

Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces

This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces,

Authors: Dan Fu and Wei Ding

Double almost statistical convergence of order α

The goal of this paper is to define and study λ-double almost statistical convergence of order α. Further some inclusion relations are examined. We also introduce a new sequence space by combining the double almo...

Authors: Ekrem Savaş