Articles

On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term

Li et al. (SIAM J. Sci. Comput. 20:719–738, 1998) used the moving mesh partial differential equation (MMPDE) to solve a scaled Fisher’s equation and the initial condition consisting of an exponential function. Th...

Authors: K. M. Agbavon, A. R. Appadu and M. Khumalo

Bernoulli F-polynomials and Fibo–Bernoulli matrices

In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbe...

Authors: Semra Kuş, Naim Tuglu and Taekyun Kim

Dynamical analysis of a fractional SIRS model on homogenous networks

Authors: H. A. A. El-Saka, A. A. M. Arafa and M. I. Gouda

Note on weakly fractional differential equations

In this paper, we compare solutions of q-order fractional differential equations of Caputo type for q near 1 with solutions of the corresponding 1-order ordinary differential equations. By establishing the explic...

Authors: Michal Fečkan, Michal Pospíšil and JinRong Wang

Multiple positive solutions for perturbed nonlinear fractional differential system with two control parameters

In this paper, we study a class of perturbed nonlinear fractional differential systems with two control parameters. Under some appropriate conditions on the primitive function of nonlinear terms

Authors: Yulin Zhao, Xiaoyan Shi and Liang Tang

Curved beam elasticity theory based on the displacement function method using a finite difference scheme

A displacement function suitable for plane curved beam in polar coordinates is introduced, and a partial differential governing equation of plane curved beam is obtained by theoretical analysis. Then, the form...

Authors: Wankui Bu and Hui Xu

Dissipative criteria for Takagi–Sugeno fuzzy Markovian jumping neural networks with impulsive perturbations using delay partitioning approach

In this work, we investigate the result of dissipative analysis for Takagi–Sugeno fuzzy Markovian jumping neural networks with impulsive perturbations via delay partition approach. By using the Lyapunov–Krasov...

Authors: V. J. Nirmala, T. Saravanakumar and Quanxin Zhu

Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions

In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as B...

Authors: Aphirak Aphithana, Sotiris K. Ntouyas and Jessada Tariboon

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

We propose a new chaotic financial system by considering ethics involvement in a four-dimensional financial system with market confidence. We present a five-dimensional conformable derivative financial system ...

Authors: Baogui Xin, Wei Peng, Yekyung Kwon and Yanqin Liu

On the boundedness of poles of generalized Padé approximants

Given a function F holomorphic on a neighborhood of some compact subset of the complex plane, we prove that if the zeros of the denominators of generalized Padé approximants (orthogonal Padé approximants and Padé...

Authors: Nattapong Bosuwan

Causal difference equations with upper and lower solutions in the reverse order

This paper is devoted to studying the existence conditions for difference equations involving causal operators in the presence of upper and lower solutions in the reverse order. To this end, we prove some new ...

Authors: Wen-Li Wang and Jing-Feng Tian

Existence and uniqueness of the global solution for a class of nonlinear fractional integro-differential equations in a Banach space

In this paper, by employing fixed point theory, we investigate the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations on semi-infinite domains in a Banach ...

Authors: Peiguo Zhang, Xinan Hao and Lishan Liu

The construction of solutions to Zakharov–Kuznetsov equation with fractional power nonlinear terms

In the paper, we study a plasma fluid physical model, namely the Zakharov–Kuznetsov (ZK, for simplicity) equation with fractional power nonlinear terms by the complete discrimination system for polynomial meth...

Authors: Yang Liu and Xin Wang

One kind of character sum modulo a prime p and its recurrence formula

The aim of this paper is to use an analytic method and the properties of the classical Gauss sums to research the computational problem of one kind of character sum of polynomials modulo an odd prime p and obtain...

Authors: Wenpeng Zhang and Zhuoyu Chen

On existence and continuation of solutions of the state-dependent impulsive dynamical system with boundary constraints

The state-dependent impulsive dynamical system with boundary constraints is a kind of special but common system in nature. But because of the complexity of the geometry or topological structures of the impulsi...

Authors: Ling Chen, Zhi Long He, Chuan Dong Li and Hafiz Gulfam Ahmad Umar

Lyapunov inequalities of left focal q-difference boundary value problems and applications

In this paper, we establish some Lyapunov-type inequalities for a class of linear and nonlinear fractional q-difference boundary value problems under Cauchy boundary conditions. As applications, we use the inequa...

Authors: Lulu Zhang, Yige Zhao and Shurong Sun

Some dynamic inequalities on time scales and their applications

Authors: A. A. El-Deeb, Haiyong Xu, A. Abdeldaim and Guotao Wang

A connection between weighted Hardy’s inequality and half-linear dynamic equations

In this paper, we give an affirmative answer to the following question: Is the solvability of some nonlinear dynamic equations on a time scale

Authors: S. H. Saker and R. R. Mahmoud

Existence of positive solution to a coupled system of singular fractional difference equations via fractional sum boundary value conditions

In this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by e...

Authors: Chanon Promsakon, Saowaluck Chasreechai and Thanin Sitthiwirattham

Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets

In this paper, we present a semi-analytic method called the local fractional homotopy analysis method (LFHAM) for solving differential equations involving local fractional derivatives based on the local fracti...

Authors: Shehu Maitama and Weidong Zhao

Bifurcations and exact traveling wave solutions for a modified Degasperis–Procesi equation

In this paper, the bifurcations of a modified Degasperis–Procesi equation are studied under different parametric conditions, which have not been investigated by the bifurcation theory of dynamical systems befo...

Authors: Minzhi Wei

Fractional hybrid differential equations with three-point boundary hybrid conditions

In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order

Authors: Choukri Derbazi, Hadda Hammouche, Mouffak Benchohra and Yong Zhou

Bifurcation analysis of a two-dimensional discrete Hindmarsh–Rose type model

In this paper, bifurcation analysis of a discrete Hindmarsh–Rose model is carried out in the plane. This paper shows that the model undergoes a flip bifurcation, a Neimark–Sacker bifurcation, and

Authors: Bo Li and Qizhi He

A new result on stability analysis for discrete system with interval time-varying delays

This paper is concerned with the stability criteria for a discrete-time linear system with interval time-varying delays. By using the time delay division we construct an augmented Lyapunov–Krasovskii functiona...

Authors: Daixi Liao, Shouming Zhong, Jun Cheng, Can Zhao, Xiaojun Zhang and Yongbin Yu

The fractional form of a new three-dimensional generalized Hénon map

In this paper, we propose a fractional form of a new three-dimensional generalized Hénon map and study the existence of chaos and its control. Using bifurcation diagrams, phase portraits and Lyapunov exponents...

Authors: Lotfi Jouini, Adel Ouannas, Amina-Aicha Khennaoui, Xiong Wang, Giuseppe Grassi and Viet-Thanh Pham

The classification of the single traveling wave solutions to \((1+1)\) dimensional Gardner equation with variable coefficients

Authors: Damin Cao and Lijuan Du

State bounding estimation for a linear continuous-time singular system with time-varying delay

This paper investigates the problem of a state bounding estimation for a linear continuous-time singular system with time-varying delay. By employing the maximal Lyapunov–Krasovskii functional and applying the...

Authors: Jianying Xiao and Fang Xu

Anti-periodic boundary value problems with Riesz–Caputo derivative

This paper is concerned with a class of anti-periodic boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which can reflected both the past and the future nonlocal m...

Authors: Fulai Chen, Anping Chen and Xia Wu

On the oscillation of fourth-order delay differential equations

Authors: Said R. Grace, Jozef Džurina, Irena Jadlovská and Tongxing Li

A pest control model with birth pulse and residual and delay effects of pesticides

Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed t...

Authors: Jinyang Li, Qingdao Huang and Bing Liu

Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and c...

Authors: Lin He and Juncheng Lv

Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method

A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives...

Authors: Mohamed R. Ali, Adel R. Hadhoud and H. M. Srivastava

A note on entire functions sharing a finite set with their difference operators

In this note, we will show that an entire function is equal to its difference operator if it has a growth property and shares a set, where the set consists of two entire functions of smaller orders. This result g...

Authors: Jianming Qi, Yanfeng Wang and Yongyi Gu

Legendre spectral element method for solving sine-Gordon equation

In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize...

Authors: Mahmoud Lotfi and Amjad Alipanah

Multiple positive solutions for nonlinear mixed fractional differential equation with p-Laplacian operator

In this article, multiple positive solutions are considered for nonlinear mixed fractional differential equations with a p-Laplacian operator. Using the Avery–Peterson fixed point theorem, we conclude to the exis...

Authors: Yunhong Li

Stability of a stochastic discrete mutualism system

Under the assumption that stochastic white noise perturbations are directly proportional to the deviation of the state from the equilibrium states of a continuous mutualistic model, we use the Euler–Maruyama d...

Authors: Xinyuan Liao and Yuming Chen

Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. As a generalization of this, we ...

Authors: Taekyun Kim, Dae San Kim, Dmitry V. Dolgy and Dojin Kim

Wave propagation in a infectious disease model with non-local diffusion

In this paper, we propose a nonlocal diffusion infectious disease model with nonlinear incidences and distributed delay to model the transmission of the epidemic. By a fixed point theorem and a limiting argume...

Authors: Yueling Cheng and Dianchen Lu

On numerical techniques for solving the fractional logistic differential equation

This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solut...

Authors: Yves Yannick Yameni Noupoue, Yücel Tandoğdu and Muath Awadalla

Bifurcation analysis for the Kaldor–Kalecki model with two delays

In this paper, a Kaldor–Kalecki model of business cycle with two discrete time delays is considered. Firstly, by analyzing the corresponding characteristic equations, the local stability of the positive equili...

Authors: Cao Jianzhi and Sun Hongyan

Periodic solutions for p-Laplacian neutral differential equation with multiple delay and variable coefficients

Authors: Zhonghua Bi, Zhibo Cheng and Shaowen Yao

On the existence and uniqueness of \((N,\lambda )\)-periodic solutions to a class of Volterra difference equations

Authors: Edgardo Alvarez, Stiven Díaz and Carlos Lizama

Existence of positive solution and Hyers–Ulam stability for a nonlinear singular-delay-fractional differential equation

In this article, we consider a study of a general class of nonlinear singular fractional DEs with p-Laplacian for the existence and uniqueness (EU) of a positive solution and the Hyers–Ulam (HU) stability. To pro...

Authors: Hasib Khan, Thabet Abdeljawad, Muhammad Aslam, Rahmat Ali Khan and Aziz Khan

G-stability one-leg hybrid methods for solving DAEs

This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are som...

Authors: P. Agarwal, Iman H. Ibrahim and Fatma M. Yousry

Multiple positive solutions for a coupled system of nonlinear impulsive fractional differential equations with parameters

We consider the multiplicity of positive solutions (PSs) for a coupled system involving nonlinear impulsive fractional differential equations with parameters. By employing the classical Guo–Krasnosel’skii fixe...

Authors: Kun Wang and Ping Gong

Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations

In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to o...

Authors: Arshad Ali, Kamal Shah, Fahd Jarad, Vidushi Gupta and Thabet Abdeljawad

Variational method to a fractional impulsive \((p,q)\)-Laplacian coupled systems with partial sub-\((p,q)\) linear growth

In this paper, by using the least action principle, an existence result of nontrivial weak solutions for a class of fractional impulsive coupled systems with ...

Authors: Cuiling Liu, Xingyong Zhang and Junping Xie

Hopf bifurcation analysis in a predator–prey model with time delay and food subsidies

We analyze the stability of positive equilibrium in a predator-prey model with time delay τ and subsidies. The sufficient conditions of the local Hopf bifurcations at the positive equilibrium are obtained. By cen...

Authors: Yuxiao Guo, Nannan Ji and Ben Niu

A higher-order blended compact difference (BCD) method for solving the general 2D linear second-order partial differential equation

A higher-order blended compact difference (BCD) scheme is proposed to solve the general two-dimensional (2D) linear second-order partial differential equation. The distinguishing feature of the present method ...

Authors: Tingfu Ma and Yongbin Ge

Local fractional system for economic order quantity using entropy solution

The economic order quantity (EOQ) model describes the quantity that minimizes the aggregate sum of all cost functions. We propose an assembly for EOQ, nonlinear local fractional differential models with costs ...

Authors: Rabha W. Ibrahim, Hossein Jafari, Hamid A. Jalab and Samir B. Hadid