Articles

Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under...

Authors: Aliyu Isa Aliyu, Ali Saleh Alshomrani, Yongjin Li, Mustafa Inc and Dumitru Baleanu

Stability of discrete-time HIV dynamics models with three categories of infected CD4⁺ T-cells

This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected ce...

Authors: A. M. Elaiw and M. A. Alshaikh

Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion

In the literature, many generalizations of continued fractions have been introduced, and for each of them, convergence results have been proved. In this paper, we suggest a definition of generalized continued ...

Authors: Hendrik Baumann

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with im...

Authors: Najeeb Alam Khan, Oyoon Abdul Razzaq, Sankar Parsad Mondal and Qammar Rubbab

Oscillation and nonoscillation theorems of neutral dynamic equations on time scales

Authors: Yong Zhou, Ahmed Alsaedi and Bashir Ahmad

Endpoint regularity of discrete multilinear fractional nontangential maximal functions

Authors: Daiqing Zhang

Study of nonlinear Pachpatte’s inequalities on time scales

In this paper, we develop a fundamental dynamic inequality, a generalization of comparison theorem and reproduce the proofs of some nonlinear integral Pachpatte’s inequalities by using their continuous analogu...

Authors: Sarah Sarfaraz, Naveed Ahmad and Ghaus ur Rahman

Non-linear population discrete models with two time scales: re-scaling of part of the slow process

In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in prac...

Authors: Luis Sanz, Rafael Bravo de la Parra, Marcos Marvá and Eva Sánchez

A stabilized coupled method and its optimal error estimates for elliptic interface problems

In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provi...

Authors: Jiaping Yu, Feng Shi and Jianping Zhao

Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure

Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems....

Authors: Tousheng Huang, Huayong Zhang, Zhengran Hu, Ge Pan, Shengnan Ma, Xiumin Zhang and Zichun Gao

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

We show that the Stirling numbers of the first and second kind can be represented in terms of moments of appropriate random variables. This allows us to obtain, in a unified way, a variety of old and new expli...

Authors: José A. Adell and Alberto Lekuona

Neimark–Sacker bifurcation of a chemotherapy treatment of glioblastoma multiform (GBM)

In this paper, we propose a system of differential equations with piecewise constant arguments to describe the growth of GBM under chemotherapeutic treatment and the interaction among the glial cells, the canc...

Authors: F. Bozkurt and A. Yousef

Numerical solution of stochastic state-dependent delay differential equations: convergence and stability

Numerical analysis of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple feature. In this paper, we aim to study a more general cas...

Authors: Bahar Akhtari

A non-autonomous impulsive food-chain model with delays

A non-autonomous almost periodic prey–predator system with impulsive effects and multiple delays is proposed in this paper, Holling’s type-IV systems and ratio-dependent functional responses are also involved ...

Authors: Baodan Tian, Pengkai Zhang, Jiamei Li, Yong Zhang and Liu Yang

Unique solution for a new system of fractional differential equations

Authors: Chengbo Zhai and Xiaolin Zhu

Weighted dynamic inequalities of Opial-type on time scales

In this paper, we will state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in th...

Authors: A. A. El-Deeb, Fatma M. Kh, Gamal A. F. Ismail and Zareen A. Khan

On characteristic polynomial of higher order generalized Jacobsthal numbers

Authors: Diego Marques and Pavel Trojovský

Fractional-calculus-based control scheme for dynamical systems with input uncertainty

Since the existence of unwanted oscillations should be avoided in practical systems, this article investigates active vibration and oscillation suppression of two-degree-of-freedom dynamical systems using a no...

Authors: Mohammad Pourmahmood Aghababa

Outer-synchronization of fractional-order neural networks with deviating argument via centralized and decentralized data-sampling approaches

This paper is committed to investigating outer-synchronization of fractional-order neural networks with deviating argument via centralized and decentralized data-sampling approaches. Considering the low cost a...

Authors: Weike Cheng, Ailong Wu, Jin-E Zhang and Biwen Li

Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions

Using the monotone iterative technique, we investigate the existence of iterative positive solutions to a coupled system of fractional differential equations supplemented with multistrip and multipoint mixed b...

Authors: Xiaodi Zhao, Yuehan Liu and Huihui Pang

Oscillation of fourth-order strongly noncanonical differential equations with delay argument

Authors: B. Baculikova and J. Dzurina

Some new weakly singular integral inequalities with discontinuous functions for two variables and their applications

This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative analysis o...

Authors: Yaoyao Luo and Run Xu

An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, di...

Authors: Aydin Secer and Neslihan Ozdemir

Stochastic bifurcation analysis in Brusselator system with white noise

In this paper, we mainly study the stochastic stability and stochastic bifurcation of Brusselator system with multiplicative white noise. Firstly, by a polar coordinate transformation and a stochastic averagin...

Authors: Changzhao Li and Juan Zhang

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

We consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy–Schwartz i...

Authors: Ardak Kashkynbayev, Jinde Cao and Zhaksybek Damiyev

Mixed \(H_{\infty }/\)passive exponential function projective synchronization of delayed neural networks with hybrid coupling based on pinning sampled-data control

Authors: Thongchai Botmart, Narongsak Yotha, Piyapong Niamsup, Wajaree Weera and Prem Junsawang

Positive solutions of singular Hadamard-type fractional differential equations with infinite-point boundary conditions or integral boundary conditions

We establish the existence of positive solutions to a class of a singular nonlinear Hadamard-type fractional differential equations with infinite-point boundary conditions (BCs) or integral BCs. Our analysis i...

Authors: A. M. A. El-Sayed and F. M. Gaafar

A dynamically consistent nonstandard finite difference scheme for a predator–prey model

The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-ove...

Authors: Muhammad Sajjad Shabbir, Qamar Din, Muhammad Safeer, Muhammad Asif Khan and Khalil Ahmad

Variance-constrained resilient \(H_{\infty }\) state estimation for time-varying neural networks with randomly varying nonlinearities and missing measurements

Authors: Yan Gao, Jun Hu, Dongyan Chen and Junhua Du

The logarithmic concavity of modified Bessel functions of the first kind and its related functions

This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties. One of o...

Authors: Thanit Nanthanasub, Boriboon Novaprateep and Narongpol Wichailukkana

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping t...

Authors: Nauman Khalid, Muhammad Abbas, Muhammad Kashif Iqbal and Dumitru Baleanu

Numerical approximation of the fractional HIV model using the meshless local Petrov–Galerkin method

This paper deals with the model of fractional HIV-1 infection of CD4⁺T cells transformation with homogeneous Neumann boundary conditions. Numerical methods for solving fractional time differential equations are d...

Authors: Kunwithree Phramrung, Anirut Luadsong and Nitima Aschariyaphotha

Shifts, rotations and distributional chaos

Authors: Dongsheng Xu, Kaili Xiang and Shudi Liang

On some results in intuitionistic fuzzy ideal convergence double sequence spaces

Recently, spaces of ideal convergent sequences of bounded linear operators were studied by Khan et al. (Numer. Funct. Anal. Optim. 39:1278-1290, 2018). This has motivated us to propose the intuitionistic fuzzy I-...

Authors: Vakeel A. Khan, Mobeen Ahmad, Hira Fatima and Mohd Faisal Khan

Continuum-wise expansive homoclinic classes for robust dynamical systems

Authors: Manseob Lee

A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality...

Authors: Jian Li, Haibiao Zheng and Qingsong Zou

Positive radial solutions of n-dimensional elliptic systems with indefinite weight functions and n parameters

Under simple conditions on f and a, we show the existence of positive radial solutions for the n-dimensional elliptic differential system

Authors: Meiqiang Feng and Ping Li

Uniqueness of meromorphic solutions sharing values with a meromorphic function to \(w(z + 1)w(z - 1) = h(z)w^{m}(z)\)

Authors: BaoQin Chen and Sheng Li

Asymptotically almost periodic mild solutions to a class of Weyl-like fractional difference equations

This paper is concentrated on a class of difference equations with a Weyl-like fractional difference in a Banach space X forms like

Authors: Junfei Cao, Bessem Samet and Yong Zhou

Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

In this paper, by introducing the fractional derivatives in the sense of Caputo, the modified general mapping deformation method (MGMDM) and the modified fractional variational iteration method (MFVIM) are app...

Authors: Baojian Hong, Dianchen Lu and Wei Chen

Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response

In this paper, a prey-predator model with Allee effect and Holling type-I functional response is established, and its dynamical behaviors are studied in detail. The existence, boundedness and stability of the ...

Authors: Yong Ye, Hua Liu, Yumei Wei, Kai Zhang, Ming Ma and Jianhua Ye

Effect of pulse vaccination on dynamics of dengue with periodic transmission functions

Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In t...

Authors: Rashid Jan and Yanni Xiao

An efficient iterative approach for three-dimensional modified anomalous fractional sub-diffusion equations on a large domain

The fractional sub-diffusion equation, which is obtained by replacing the time derivative in ordinary diffusion by a fractional derivative of order ϑ with ...

Authors: Zhonglian Ma, Mohammad Hossein Heydari, Zakieh Avazzadeh and Carlo Cattani

Correction to: A numerical study of oil spill spreading in the Gulf of Thailand

After publication of this article [1], it was brought to our attention that the article type should be “Research” rather than “Review”.

Authors: Kittipong Srikhaetai, Kittisak Chayantrakom and Wattana Kanbua

Extended cubic B-splines in the numerical solution of time fractional telegraph equation

A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization...

Authors: Tayyaba Akram, Muhammad Abbas, Ahmad Izani Ismail, Norhashidah Hj. M. Ali and Dumitru Baleanu

Complete monotonicity related to the k-polygamma functions with applications

In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.

Authors: Li Yin, Jumei Zhang and XiuLi Lin

Identifying weak focus of order 3 in a Leslie–Gower prey–predator model with prey harvesting

In this paper, we identify a weak focus with order up to 3 for a Leslie–Gower prey–predator model with three parameters. The known work computed the first Lyapunov quantity and discussed Hopf bifurcations of t...

Authors: Juan Su

Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations

Liouville–Green (WKB) asymptotic approximations are constructed for some classes of linear second-order difference equations. This is done starting from certain “canonical forms” for the three-term linear recurre...

Authors: Renato Spigler

A stochastic predator–prey model for integrated pest management

This paper studies a stochastic predator–prey model for integrated pest management. It shows that the system has a positive solution that exists globally. The long time behavior of the system is investigated, ...

Authors: Lidong Huang, Xingshu Chen, Xuewen Tan, Xiaochou Chen and Xinzhi Liu

Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism

A Lotka–Volterra predator–prey model incorporating predator cannibalism is proposed and studied in this paper. The existence and stability of all possible equilibria of the system are investigated. Our study s...

Authors: Hang Deng, Fengde Chen, Zhenliang Zhu and Zhong Li