Articles

Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispe...

Authors: Hui Zhou, Jehad Alzabut, Shahram Rezapour and Mohammad Esmael Samei

Nonlinear integral inequality with power and its application in delay integro-differential equations

New nonlinear integral inequalities (NII) are presented in this paper. Based on mathematical analysis technique, several estimation results are obtained, which not only complement the aforementioned results, b...

Authors: Yazhou Tian and Min Fan

Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set...

Authors: Taherh Tahernezhad and Reza Jalilian

Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

Authors: Hojjat Afshari and Dumitru Baleanu

Study of implicit delay fractional differential equations under anti-periodic boundary conditions

This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory d...

Authors: Arshad Ali, Kamal Shah and Thabet Abdeljawad

Fractional spectral differentiation matrices based on Legendre approximation

Authors: Asghar Ghorbani and Dumitru Baleanu

Generalized fractional integral inequalities of Hermite–Hadamard type for harmonically convex functions

In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained res...

Authors: Dafang Zhao, Muhammad Aamir Ali, Artion Kashuri and Hüseyin Budak

Square-mean piecewise almost automorphic mild solutions to a class of impulsive stochastic evolution equations

In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean ...

Authors: Junwei Liu, Ruihong Ren and Rui Xie

Shannon type inequalities via time scales theory

The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen’s inequality in time scales settings. The concept of differential entropy of a continuous random variable on...

Authors: Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Ðilda Pečarić and Josip Pečarić

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Authors: C. Koroglu

New approaches for the solution of space-time fractional Schrödinger equation

The aim of this study is to establish the solution of the time-space fractional Schrödinger equation subject to initial and boundary conditions which has many applications in science such as nonlinear optics, ...

Authors: Ali Demir, Mine Aylin Bayrak and Ebru Ozbilge

Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme

In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonl...

Authors: Sunyoung Bu and Soyoon Bak

Retraction Note to: Existence of weak solutions for two point boundary value problems of Schrödingerean predator-prey system and their applications

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors that was simultaneously under consideration with another journal [2]. In addition, th...

Authors: Fengjiao Lü and Tanriver Ülker

Attractivity for Hilfer fractional stochastic evolution equations

This article is devoted to the study of the attractivity of solutions to a class of stochastic evolution equations involving Hilfer fractional derivative. By employing the semigroup theory, fractional calculus...

Authors: Min Yang, Ahmed Alsaedi, Bashir Ahmad and Yong Zhou

Stability and bifurcation in a single species logistic model with additive Allee effect and feedback control

In this paper, we propose a single species logistic model with feedback control and additive Allee effect in the growth of species. The basic aim of the paper is to discuss how the additive Allee effect and fe...

Authors: Yangyang Lv, Lijuan Chen and Fengde Chen

Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain

In this paper, we deal with the inverse problem of identifying the unknown source of time-fractional diffusion equation on a columnar symmetric domain. This problem is ill-posed. Firstly, we establish the cond...

Authors: Fan Yang, Pan Zhang, Xiao-Xiao Li and Xin-Yi Ma

Parameter identification of genetic regulatory network with time-varying delays via adaptive synchronization method

In this paper, the parameter identification of gene regulatory network with time-varying delay is studied. Firstly, we introduce the differential equation model of gene regulatory network with unknown paramete...

Authors: Chunlin Liu and Fei Wang

Nonlocal-derivative NLS equations and group-invariant soliton solutions

Authors: Yuqin Yao and Yehui Huang

On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals

Authors: Saima Rashid, Fahd Jarad, Humaira Kalsoom and Yu-Ming Chu

Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators

Stochastic differential models provide an additional degree of realism compared to their corresponding deterministic counterparts because of the randomness and stochasticity of real life. In this work, we stud...

Authors: Fathalla A. Rihan and Hebatallah J. Alsakaji

Global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies system involving multiple pairs of time-varying delays

In our article, a nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure has been investigated, in which the delays are time-varying and multiple pairs. Based upon the fluctuat...

Authors: Yanli Xu and Qian Cao

On Hilfer fractional difference operator

In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer di...

Authors: Syed Sabyel Haider, Mujeeb ur Rehman and Thabet Abdeljawad

Finite-time adaptive neural network control for fractional-order chaotic PMSM via command filtered backstepping

A finite-time adaptive neural network position tracking control method is considered for the fractional-order chaotic permanent magnet synchronous motor (PMSM) via command filtered backstepping in this paper. ...

Authors: Senkui Lu, Xingcheng Wang and Longda Wang

Dynamics analysis on a class of delayed neural networks involving inertial terms

This paper explores a class of unbounded distributed delayed inertial neural networks. By introducing some new differential inequality analysis and abandoning the traditional order reduction technique, some ne...

Authors: Jian Zhang and Chuangxia Huang

The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives

In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Us...

Authors: Mohamed S. Abdel Latif, Abass H. Abdel Kader and Dumitru Baleanu

Formal and analytic normal forms for non-autonomous difference systems with uniform dichotomy spectrum

In this paper, we extend formal and analytic normal forms from autonomous difference systems to non-autonomous ones based on the uniform dichotomy spectrum of their linear part.

Authors: Ren Zhihua, Wang Peirong, Xu Yanqin and Wu Hao

Dynamical analysis of a stochastic toxin-producing phytoplankton–fish system with harvesting

In this paper, we analytically and numerically study the dynamics of a stochastic toxin-producing phytoplankton–fish system with harvesting. Mathematically, we give the existence and stability of the positive ...

Authors: Tiancai Liao, Chuanjun Dai, Hengguo Yu, Zengling Ma, Qi Wang and Min Zhao

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is...

Authors: Min Sun and Jing Liu

Degenerate binomial coefficients and degenerate hypergeometric functions

In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients. In more detail, we introduce degenerate gener...

Authors: Taekyun Kim, Dae San Kim, Hyunseok Lee and Jongkyum Kwon

Existence uniqueness and stability of mild solutions for semilinear ψ-Caputo fractional evolution equations

In this paper, we study the local and global existence, and uniqueness of mild solution to initial value problems for fractional semilinear evolution equations with compact and noncompact semigroup in Banach s...

Authors: Apassara Suechoei and Parinya Sa Ngiamsunthorn

New model of May cooperative system with strong and weak cooperative partners

In this paper, based on the model of Zhao, Qin, and Chen [Adv. Differ. Equ. 2018:172, 2018], we propose a new model of the May cooperative system with strong and weak cooperative partners. The model overcomes the...

Authors: Qifa Lin, Chaoquan Lei, Shuwen Luo and Yalong Xue

Growth of solutions to two systems of q-difference differential equations

This paper is devoted to studying the growth of entire or meromorphic solutions to two systems of q-difference differential equations. The estimates on the growth order of meromorphic solutions are obtained, whic...

Authors: Hongqiang Tu and Wenjun Yuan

Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives

Authors: Hojjat Afshari, Mojtaba Sajjadmanesh and Dumitru Baleanu

Matrix transformations of Norlund–Orlicz difference sequence spaces of nonabsolute type and their Toeplitz duals

Authors: Adem Kılıçman and Kuldip Raj

A 3SI3R model for the propagation of two rumors with mutual promotion

There are often many kinds of rumors spreading in new media after emergencies; however, the existing studies have focused on the rumors with competition, and little attention has been paid to those with mutual...

Authors: Zhiying Wang, Jing Liang, Huifang Nie and Hongli Zhao

Certain properties of difference operator and stability of Fréchet functional equation

Authors: Teerapol Sukhonwimolmal

Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge

In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, suffi...

Authors: Yantao Luo, Long Zhang, Zhidong Teng and Tingting Zheng

Sufficient conditions for regular solvability of an arbitrary order operator-differential equation with initial-boundary conditions

Authors: Nashat Faried, Abdel Baset I. Ahmed and Mohamed A. Labeeb

Stability of Ulam–Hyers and Ulam–Hyers–Rassias for a class of fractional differential equations

In this paper, we investigate a class of nonlinear fractional differential equations with integral boundary condition. By means of Krasnosel’skiĭ fixed point theorem and contraction mapping principle we prove ...

Authors: Qun Dai, Ruimei Gao, Zhe Li and Changjia Wang

Central limit theorem for a fractional stochastic heat equation with spatially correlated noise

Authors: Yumeng Li

Quantum Hermite–Hadamard inequality by means of a Green function

The purpose of this work is to present the quantum Hermite–Hadamard inequality through the Green function approach. While doing this, we deduce some novel quantum identities. Using these identities, we establi...

Authors: Muhammad Adil Khan, Noor Mohammad, Eze R. Nwaeze and Yu-Ming Chu

Impulsive quantum \((p,q)\)-difference equations

Authors: Thana Nuntigrangjana, Sasitorn Putjuso, Sotiris K. Ntouyas and Jessada Tariboon

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investi...

Authors: A. Pratap, R. Raja, Jinde Cao, J. Alzabut and Chuangxia Huang

Certain fractional conformable inequalities for the weighted and the extended Chebyshev functionals

The main aim of this present paper is to establish fractional conformable inequalities for the weighted and extended Chebyshev functionals. We present some special cases of our main result in terms of the Riem...

Authors: Asifa Tassaddiq, Gauhar Rahman, Kottakkaran Sooppy Nisar and Muhammad Samraiz

Finite-time \(H_{\infty }\) bounded control of networked control systems with mixed delays and stochastic nonlinearities

Authors: Ling Hou, Dongyan Chen and Chan He

A new class of travelling wave solutions for local fractional diffusion differential equations

In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local fractional vector operators and a local fractional Laplace operato...

Authors: Ziyue Shi, Wei Qi and Jing Fan

Dynamics of localized waves and interaction solutions for the \((3+1)\)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

Authors: Wenhao Liu and Yufeng Zhang

Fixed time synchronization of delayed quaternion-valued memristor-based neural networks

This paper investigates the fixed time synchronization issue for a class of quaternion-valued memristor-based neural networks (QVMNN) at the presence of time varying delays. Differential inclusion and fixed ti...

Authors: Dingyuan Chen, Weiwei Zhang, Jinde Cao and Chuangxia Huang

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

Authors: Qingjun Lou and Yupeng Qin

On the Chebyshev polynomials and some of their new identities

The main purpose of this paper is, using the elementary methods and properties of the power series, to study the computational problem of the convolution sums of Chebyshev polynomials and Fibonacci polynomials...

Authors: Di Han and Xingxing Lv