Articles

Bivariate Bernstein–Schurer–Stancu type GBS operators in \((p,q)\)-analogue

Authors: M. Mursaleen, Mohd. Ahasan and K. J. Ansari

Note on the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate

We revisit the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate. By using the differential inequality theory and Bendixson–Dulac criteri...

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

Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

In this paper, bifurcations and chaotic behaviours of Kopel oligopoly model with different adjustment speed are discussed. The results imply that the Kopel oligopoly model undergoes flip bifurcation, Neimark–S...

Authors: Bo Li, Qizhi He and Ruoyu Chen

A study of coupled systems of mixed order fractional differential equations and inclusions with coupled integral fractional boundary conditions

In this work we investigate existence and uniqueness of solutions for new coupled systems of mixed order fractional differential equations and inclusions supplemented with coupled nonlocal fractional boundary ...

Authors: Sotiris K. Ntouyas and Hamed H. Al-Sulami

Analysis of the model of HIV-1 infection of \(CD4^{+}\) T-cell with a new approach of fractional derivative

By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fi...

Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

A stochastic SIR epidemic model with Lévy jump and media coverage

A stochastic susceptible–infectious–recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global posit...

Authors: Yingfen Liu, Yan Zhang and Qingyun Wang

Modification of certain fractional integral inequalities for convex functions

We consider the modified Hermite–Hadamard inequality and related results on integral inequalities, in the context of fractional calculus using the Riemann–Liouville fractional integrals. Our results generalize...

Authors: Pshtiwan Othman Mohammed and Thabet Abdeljawad

Exact solutions to the nonlinear equation in traffic congestion

In this paper, the KdV-mKdV equation is obtained via the reductive perturbation method which can be applied to model the traffic flow. To overcome the shortcomings of the traditional KdV-mKdV equation, the ori...

Authors: Cheng Li, Damin Cao and Qing Du

Application of Adomian decomposition method to nonlinear systems

In this paper, we study the Adomian decomposition method (ADM for short) including its iterative scheme and convergence analysis, which is a simple and effective technique in dealing with some nonlinear proble...

Authors: Wenjin Li and Yanni Pang

Positive solutions for some discrete semipositone problems via bifurcation theory

Authors: Man Xu and Ruyun Ma

Approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps

The objective of this paper is to investigate the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps in a Hilbert space. Nonlocal initial conditi...

Authors: A. Anguraj, K. Ravikumar and Dumitru Baleanu

Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions

This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We es...

Authors: Akbar Zada, Jehad Alzabut, Hira Waheed and Ioan-Lucian Popa

Global attractiveness and exponential stability for impulsive fractional neutral stochastic evolution equations driven by fBm

This paper is concerned with a class of fractional neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion (fBm). First, by means of the resolvent operator techniqu...

Authors: Jiankang Liu, Wei Xu and Qin Guo

The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator

Novel explicit wave solutions are constructed for the Kudryashov–Sinelshchikov (KS) equation through liquid–gas bubbles mix under the thermodynamic conditions. A new fractional definition (Atangana–Baleanu der...

Authors: Chen Yue, Mostafa M. A. Khater, Raghda A. M. Attia and Dianchen Lu

A reduced order extrapolating technique of solution coefficient vectors to collocation spectral method for telegraph equation

In this article, we mainly develop a reduced order extrapolating model for the solution coefficient vectors of the classical collocation spectral (CCS) scheme to the two-dimensional (2D) telegraph equation by ...

Authors: Hui Wang, Qingfang He and Zhendong Luo

The resonance behavior for the coupling of two Aw–Rascle traffic models

By studying the Riemann problem for the Aw–Rascle traffic model with different pressure laws, which is the coupling of two one-dimensional hyperbolic systems, we investigate the resonance phenomena. The main d...

Authors: Yanbo Hu and Guodong Wang

On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications

This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. The continuous dependence of the solution on the set of selections of...

Authors: Ahmed Mohamed El-Sayed and Shorouk Mahmoud Al-Issa

A bifurcation and symmetry result for critical fractional Laplacian equations involving a perturbation

In the present paper, by using the variational and topological methods, we obtain a multiplicity and bifurcation result for the following fractional problems involving critical nonlinearities and a lower order...

Authors: Jiabin Zuo, Mingwei Li, Bomeng Li and Zhenhua Qiao

Impulsive stochastic fractional differential equations driven by fractional Brownian motion

In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional ...

Authors: Mahmoud Abouagwa, Feifei Cheng and Ji Li

Retraction Note to: Normal families and asymptotic behaviors for solutions of certain Laplace equations

The Editors-in-Chief have retracted this article [1] because it shows significant overlap with an article by different authors that was simultaneously under consideration with another journal [2] and with a pr...

Authors: Zhenhai Yan and Beatriz Ychussie

Analyzing transient response of the parallel RCL circuit by using the Caputo–Fabrizio fractional derivative

In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fra...

Authors: Shahram Alizadeh, Dumitru Baleanu and Shahram Rezapour

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The inciden...

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

Numerical analysis for time-fractional Schrödinger equation on two space dimensions

In this paper, we study the numerical methods for solving the time-fractional Schrödinger equation (TFSE) with Caputo or Riemann–Liouville fractional derivative. The numerical schemes are implemented by using ...

Authors: Jun Zhang, JinRong Wang and Yong Zhou

Using of PQWs for solving NFID in the complex plane

We approximate the solution of the nonlinear Fredholm integro-differential equation (NFID) in the complex plane by periodic quasi-wavelets (PQWs). This kind of wavelets possesses orthonormality properties, the...

Authors: M. Erfanian, H. Zeidabadi and M. Parsamanesh

Existence and uniqueness of nontrivial solution for nonlinear fractional multi-point boundary value problem with a parameter

In this paper, a class of fractional boundary value problems with a parameter are discussed. We give some sufficient conditions to guarantee that above problems have a unique solution and construct the corresp...

Authors: Yanbin Sang and Luxuan He

Impulsive control on delayed feedback chaotic financial system with Markovian jumping

In this paper, the global asymptotic stability of both the closed economy system and the open economy system is investigated under impulse control, and the obtained stability criteria improve the existing resu...

Authors: Ruofeng Rao and Shouming Zhong

Bifurcation analysis of a discrete SIR epidemic model with constant recovery

We state and study a discrete SIR epidemic model with bilinear incidence rate and constant recovery. We obtain conditions for the existence of the disease-free equilibrium and endemic equilibria. Theoretic ana...

Authors: Hui Cao, Huan Wu and Xiaoqin Wang

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the ...

Authors: Mahmoud Moustafa, Mohd Hafiz Mohd, Ahmad Izani Ismail and Farah Aini Abdullah

Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays

In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree the...

Authors: Yongkun Li and Jianglian Xiang

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear t...

Authors: Ved Prakash Dubey, Rajnesh Kumar, Devendra Kumar, Ilyas Khan and Jagdev Singh

Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model

We investigate the dynamical behavior of a modified Leslie–Gower prey–predator model with harvesting in prey population. In order to explore rich dynamics of the model, Euler approximation is implemented to ob...

Authors: Muhammad Bilal Ajaz, Umer Saeed, Qamar Din, Irfan Ali and Muhammad Israr Siddiqui

Inverse spectral problem of a class of fourth-order eigenparameter-dependent boundary value problems

This paper deals with a class of inverse spectral problems of fourth-order boundary value problems with eigenparameter-dependent boundary conditions. Under the equivalent conditions of the problem and a certai...

Authors: Ji-jun Ao and Liang Zhang

New results on global exponential stability for a periodic Nicholson’s blowflies model involving time-varying delays

This paper investigates a periodic Nicholson’s blowflies equation with multiple time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a criterion to ensure th...

Authors: Qian Cao, Guoqiu Wang and Chaofan Qian

Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

In this paper, asymptotical stability of the exact solutions of nonlinear impulsive ordinary differential equations is studied under Lipschitz conditions. Under these conditions, asymptotical stability of Rung...

Authors: Gui-Lai Zhang

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

It is important that we increase our ability for studying of complicate fractional integro-differential equation. In this paper, we investigates the existence of solutions for a pointwise defined multi-singula...

Authors: Mandana Talaee, Mehdi Shabibi, Alireza Gilani and Shahram Rezapour

Delay dynamic double integral inequalities on time scales with applications

In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As a...

Authors: Sobia Rafeeq, Humaira Kalsoom, Sabir Hussain, Saima Rashid and Yu-Ming Chu

Solution of fractional kinetic equations involving class of functions and Sumudu transform

Fractional kinetic equations (FKEs) including a wide variety of special functions have been widely and successfully applied in describing and solving many important problems of physics and astrophysics. In thi...

Authors: Kottakkaran Sooppy Nisar, Amjad Shaikh, Gauhar Rahman and Dinesh Kumar

On boundedness of unified integral operators for quasiconvex functions

This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish...

Authors: Dongming Zhao, Ghulam Farid, Muhammad Zeb, Sohail Ahmad and Kahkashan Mahreen

A kind of non-zero sum mixed differential game of backward stochastic differential equation

This paper is concerned with a non-zero sum mixed differential game problem described by a backward stochastic differential equation. Here the term “mixed” means that this game problem contains a deterministic...

Authors: Huanjun Zhang

Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo–Fabrizio fractional derivative

We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwa...

Authors: Haili Qiao, Zhengguang Liu and Aijie Cheng

On fractional \((p,q)\)-calculus

Authors: Jarunee Soontharanon and Thanin Sitthiwirattham

Numerical techniques for stochastic foot and mouth disease epidemic model with the impact of vaccination

The spread of an epidemic diseases is stochastic in nature. It is more realistic to include this stochasticity when modelling the dynamics of a communicable disease. In this paper, a stochastic model for foot ...

Authors: Kamaleldin Abodayeh, Muhammad Shoaib Arif, Ali Raza, Muhammad Rafiq, Mairaj Bibi and Amna Nazeer

The law of iterated logarithm for the estimations of diffusion-type processes

This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexit...

Authors: Mingzhi Mao and Gang Huang

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

This study investigates the finite-time synchronization of uncertain nonlinear complex dynamic networks with time-varying delay. For a class of complex network models with time-varying delay and uncertain syst...

Authors: Yiping Luo and Yuejie Yao

Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs

In this paper, we study some new Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs, which provide explicit bounds on unknown functions. These inequalities ...

Authors: Haidong Liu and Chuancun Yin

The controllability of fractional differential system with state and control delay

In this research work, we investigate the controllability of linear fractional differential control systems with state and control delay. By using an explicit solution formula, a rank criterion for controllabi...

Authors: Musarrat Nawaz, Jiang Wei and Sheng Jiale

Infinitely many solutions for a Hénon-type system in hyperbolic space

Authors: Patrícia Leal da Cunha and Flávio Almeida Lemos

A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations

This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs)...

Authors: Sunil Kumar, Amit Kumar, Syed Abbas, Maysaa Al Qurashi and Dumitru Baleanu

Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences

Authors: Elif Tan and Ho-Hon Leung

Existence of solutions for a system of singular sum fractional q-differential equations via quantum calculus

Authors: Mohammad Esmael Samei