Articles

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

Estimation of f-divergence and Shannon entropy by Levinson type inequalities via new Green’s functions and Lidstone polynomial

Authors: Muhammad Adeel, Khuram Ali Khan, Ðilda Pečarić and Josip Pečarić

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

Authors: Elif Tan and Ho-Hon Leung

The global dynamics in a wild-type and drug-resistant HIV infection model with saturated incidence

In this paper we investigate the global dynamics in an HIV virus infection model with saturated incidence. The model includes two viral strains, one is wild-type (i.e. drug sensitive) and another is drug-resis...

Authors: Wei Chen, Nafeisha Tuerxun and Zhidong Teng

Fixed point results via a Hausdorff controlled type metric

Authors: Nayab Alamgir, Quanita Kiran, Hüseyin Işık and Hassen Aydi

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

Authors: Mohammad Esmael Samei

On the finite approximate controllability for Hilfer fractional evolution systems

In this paper, we consider the finite approximate controllability of some Hilfer fractional evolution systems. Using a variational approach and Schauder’s fixed point theorem, we give sufficient conditions for...

Authors: Xianghu Liu, Yanfang Li and Guangjun Xu

An enhanced stability criterion for linear time-delayed systems via new Lyapunov–Krasovskii functionals

The stability problem of linear systems with time-varying delays is studied by improving a Lyapunov–Krasovskii functional (LKF). Based on the newly developed LKF, a less conservative stability criterion than s...

Authors: Wenyong Duan, Yan Li and Jian Chen

Boundary layer expansions for initial value problems with two complex time variables

We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptot...

Authors: A. Lastra and S. Malek

Boundedness of solutions and stability of certain second-order difference equation with quadratic term

Authors: Emin Bešo, Senada Kalabušić, Naida Mujić and Esmir Pilav

Well-posedness of stochastic modified Kawahara equation

Authors: P. Agarwal, Abd-Allah Hyder and M. Zakarya

Dynamic behaviors for a delay Lasota–Wazewska model with feedback control on time scales

In this paper, a delay Lasota–Wazewska system with feedback control on time scales is proposed. Firstly, by using some differential inequalities on time scales, sufficient conditions which ensure the permanenc...

Authors: Xiaoying Chen, Chunling Shi and Danhong Wang

Arbitrary-order economic production quantity model with and without deterioration: generalized point of view

The key objective of this paper is to study and discuss the application of fractional calculus on an arbitrary-order inventory control problem. Using the concepts of fractional calculus followed by fractional ...

Authors: Mostafijur Rahaman, Sankar Prasad Mondal, Ali Akbar Shaikh, Ali Ahmadian, Norazak Senu and Soheil Salahshour

A new high-order compact finite difference scheme based on precise integration method for the numerical simulation of parabolic equations

This paper presents two high-order exponential time differencing precise integration methods (PIMs) in combination with a spatially global sixth-order compact finite difference scheme (CFDS) for solving parabo...

Authors: Changkai Chen, Xiaohua Zhang, Zhang Liu and Yage Zhang

New approach to solutions of a class of singular fractional q-differential problem via quantum calculus

In the present article, by using the fixed point technique and the Arzelà–Ascoli theorem on cones, we wish to investigate the existence of solutions for a non-linear problems regular and singular fractional q-dif...

Authors: Sihua Liang and Mohammad Esmael Samei

Global exponential stability and existence of periodic solutions of fuzzy wave equations

In this paper, the global exponential stability and the existence of periodic solutions of fuzzy wave equations are investigated. By variable substitution the system of partial differential equations (PDEs) is...

Authors: Wei Liu and Yimin Lou

Solvability of functional-integral equations (fractional order) using measure of noncompactness

We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contract...

Authors: Reza Arab, Hemant Kumar Nashine, N. H. Can and Tran Thanh Binh

Moment estimates for invariant measures of stochastic Burgers equations

In this paper, we study moment estimates for the invariant measure of the stochastic Burgers equation with multiplicative noise. Based upon an a priori estimate for the stochastic convolution, we derive regula...

Authors: Yu Shi and Bin Liu

Dynamics analysis of a delayed virus model with two different transmission methods and treatments

In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Math. Methods Med. 201...

Authors: Tongqian Zhang, Junling Wang, Yuqing Li, Zhichao Jiang and Xiaofeng Han

A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

In this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz...

Authors: Lei Hang, Long Zhang, Xiaowen Wang, Hongli Li and Zhidong Teng

Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation

Authors: Mostafa M. A. Khater, Choonkil Park, Dianchen Lu and Raghda A. M. Attia

Oscillation results for nonlinear second order difference equations with mixed neutral terms

In this paper, we establish new oscillation criteria for nonlinear second order difference equations with mixed neutral terms. The key idea of our approach is to compare with first order equations whose oscill...

Authors: Said R. Grace and Jehad Alzabut

Synchronization control of stochastic delayed Lotka–Volterra systems with hardware simulation

In this paper, the synchronization control of a non-autonomous Lotka–Volterra system with time delay and stochastic effects is studied. The purpose is to firstly establish sufficient conditions for the existen...

Authors: Lan Wang, Yiping Dong, Da Xie and Hao Zhang

On some Hermite–Hadamard type inequalities for \(tgs\)-convex functions via generalized fractional integrals

Authors: Naila Mehreen and Matloob Anwar

Derivation of bounds of several kinds of operators via \((s,m)\)-convexity

Authors: Young Chel Kwun, Ghulam Farid, Shin Min Kang, Babar Khan Bangash and Saleem Ullah

Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations

To improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional ...

Authors: Yan Chang and Huanzhen Chen

On weighted Atangana–Baleanu fractional operators

In this paper, we define the weighted Atangana–Baleanu fractional operators of Caputo sense. We obtain the solution of a related linear fractional differential equation in a closed form, and use the result to ...

Authors: Mohammed Al-Refai

Multiple positive solutions to singular fractional differential equations with integral boundary conditions involving \(p-q\)-order derivatives

Authors: Han Wang and Jiqiang Jiang

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, w...

Authors: A. Elazzouzi, A. Lamrani Alaoui, M. Tilioua and A. Tridane

Stoichiometric knife-edge model on discrete time scale

Ecological stoichiometry is the study of the balance of multiple elements in ecological interactions and processes (Sterner and Elser in Ecological Stoichiometry: The Biology of Elements from Molecules to the ...

Authors: Ming Chen, Lale Asik and Angela Peace