Articles

Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables

This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type. By utilizin...

Authors: Hong Yan Xu, Da Wei Meng, Sanyang Liu and Hua Wang

A new construction of Lupaş operators and its approximation properties

The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences

Authors: Mohd Qasim, Asif Khan, Zaheer Abbas and Qing-Bo Cai

Mixed nonlocal boundary value problem for implicit fractional integro-differential equations via ψ-Hilfer fractional derivative

In this paper, we investigate the existence and uniqueness of a solution for a class of ψ-Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banac...

Authors: Chatthai Thaiprayoon, Weerawat Sudsutad and Sotiris K. Ntouyas

Modeling of pressure–volume controlled artificial respiration with local derivatives

We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by e...

Authors: Bahar Acay, Mustafa Inc, Yu-Ming Chu and Bandar Almohsen

On zeros and growth of solutions of complex difference equations

Authors: Min-Feng Chen and Ning Cui

Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity

In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spec...

Authors: Ruizhi Yang, Yuxin Ma and Chiyu Zhang

Correction to: Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

A Correction to this paper has been published: https://​doi.​org/​10.​1186/​s13662-020-03199-3

Authors: Fatmawati, Muhammad Altaf Khan, Cicik Alfiniyah and Ebraheem Alzahrani

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control par...

Authors: Lanre Akinyemi, Mehmet Şenol and Shaheed N. Huseen

Existence and Ulam–Hyers stability of a kind of fractional-order multiple point BVP involving noninstantaneous impulses and abstract bounded operator

In this paper, we mainly study a kind of fractional-order multiple point boundary value problem involving noninstantaneous impulse and abstract bounded operator. The existence and uniqueness is obtained by the...

Authors: Kaihong Zhao and Shoukai Deng

An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations

We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference metho...

Authors: Ihteram Ali, Sirajul Haq, Kottakkaran Sooppy Nisar and Dumitru Baleanu

Novel extended dissipativity criteria for generalized neural networks with interval discrete and distributed time-varying delays

The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapu...

Authors: Sunisa Luemsai, Thongchai Botmart and Wajaree Weera

Oscillation tests for first-order linear differential equations with non-monotone delays

We study the oscillation of a first-order linear delay differential equation. A new technique is developed and used to obtain new oscillatory criteria for differential equation with non-monotone delay. Some of...

Authors: Emad R. Attia

Uniqueness of the Hadamard-type integral equations

The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s app...

Authors: Chenkuan Li

Complexity analysis of cold chain transportation in a vaccine supply chain considering activity inspection and time-delay

The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-1...

Authors: Daoming Dai, Xuanyu Wu and Fengshan Si

Some extensions for the several combinatorial identities

In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving...

Authors: Gao-Wen Xi and Qiu-Ming Luo

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of or...

Authors: Mohammed S. Abdo, Thabet Abdeljawad, Saeed M. Ali and Kamal Shah

Construction of a new family of Fubini-type polynomials and its applications

This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introd...

Authors: H. M. Srivastava, Rekha Srivastava, Abdulghani Muhyi, Ghazala Yasmin, Hibah Islahi and Serkan Araci

Fundamental solutions for semidiscrete evolution equations via Banach algebras

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fo...

Authors: Jorge González-Camus, Carlos Lizama and Pedro J. Miana

Approximation of function using generalized Zygmund class

In this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approxi...

Authors: H. K. Nigam, Mohammad Mursaleen and Supriya Rani

A study of a coupled system of Hadamard fractional differential equations with nonlocal coupled initial-multipoint conditions

In this paper, we obtain the existence results for a coupled system of Hadamard fractional differential equations supplemented with nonlocal coupled initial-multipoint conditions via fixed point theorems. An e...

Authors: Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi and Amjad F. Albideewi

Some fractional Hermite–Hadamard-type inequalities for interval-valued coordinated functions

The primary objective of this paper is establishing new Hermite–Hadamard-type inequalities for interval-valued coordinated functions via Riemann–Liouville-type fractional integrals. Moreover, we obtain some fr...

Authors: Fangfang Shi, Guoju Ye, Dafang Zhao and Wei Liu

Dynamics of a class of host–parasitoid models with external stocking upon parasitoids

This paper is motivated by the series of research papers that consider parasitoids’ external input upon the host–parasitoid interactions. We explore a class of host–parasitoid models with variable release and ...

Authors: Jasmin Bektešević, Vahidin Hadžiabdić, Senada Kalabušić, Midhat Mehuljić and Esmir Pilav

Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions

The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defin...

Authors: Yuankui Ma, Dae San Kim, Hyunseok Lee, Hanyoung Kim and Taekyun Kim

Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approxim...

Authors: Samaira Naz, Muhammad Nawaz Naeem and Yu-Ming Chu

On the characteristic polynomial of \((k,p)\)-Fibonacci sequence

Authors: Pavel Trojovský

Stable weak solutions to weighted Kirchhoff equations of Lane–Emden type

Authors: Yunfeng Wei, Hongwei Yang and Hongwang Yu

Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative

This research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves expo...

Authors: Saeed Ahmad, Rafi Ullah and Dumitru Baleanu

Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables

In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of t...

Authors: Muhammad Aamir Ali, Yu-Ming Chu, Hüseyin Budak, Abdullah Akkurt, Hüseyin Yıldırım and Manzoor Ahmed Zahid

On a two-dimensional fractional thermoelastic system with nonlocal constraints describing a fractional Kirchhoff plate

We show herein the existence and uniqueness of solutions for coupled fractional order partial differential equations modeling a thermoelastic fractional Kirchhoff plate model associated with initial, Dirichlet...

Authors: Said Mesloub and Faten Aldosari

Hyers–Ulam stability of second-order differential equations using Mahgoub transform

The aim of this research is investigating the Hyers–Ulam stability of second-order differential equations. We introduce a new method of investigation for the stability of differential equations by using the Ma...

Authors: Antony Raj Aruldass, Divyakumari Pachaiyappan and Choonkil Park

Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

Authors: Imed Bachar, Habib Mâagli and Hassan Eltayeb

A new efficient technique for solving modified Chua’s circuit model with a new fractional operator

Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of var...

Authors: Manuel De la Sen, Sinan Deniz and Hasan Sözen

The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative

In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is ...

Authors: Salih Djilali and Behzad Ghanbari

Existence results for a coupled system of Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions...

Authors: Ahmed Alsaedi, Amjad F. Albideewi, Sotiris K. Ntouyas and Bashir Ahmad

On the weighted fractional integral inequalities for Chebyshev functionals

The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integra...

Authors: Gauhar Rahman, Kottakkaran Sooppy Nisar, Sami Ullah Khan, Dumitru Baleanu and V. Vijayakumar

Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

Authors: Adisorn Kittisopaporn, Pattrawut Chansangiam and Wicharn Lewkeeratiyutkul

Fuzzy stochastic differential equations driven by fractional Brownian motion

In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzzine...

Authors: Hossein Jafari, Marek T. Malinowski and M. J. Ebadi

Qualitative properties of mathematical model of English language education

This paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that back...

Authors: Atena Ghasemabadi and Nahid Soltanian

An efficient approach for solution of fractional-order Helmholtz equations

In this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform me...

Authors: Nehad Ali Shah, Essam R. El-Zahar, Mona D. Aljoufi and Jae Dong Chung

Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function

Authors: Abdullah Alotaibi, Faruk Özger, S. A. Mohiuddine and Mohammed A. Alghamdi

Robust stability analysis of impulsive quaternion-valued neural networks with distributed delays and parameter uncertainties

In this paper, an impulsive quaternion-valued neural networks (QVNNs) model with leakage, discrete, and distributed delays is considered. Based on the homeomorphic mapping method, Lyapunov stability theorem, a...

Authors: Jielin Zhou, Yuanshun Tan, Xiaofeng Chen and Zijian Liu

Dynamics analysis of an online gambling spreading model on scale-free networks

Nowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynami...

Authors: Yu Kong, Tao Li, Yuanmei Wang, Xinming Cheng, He Wang and Yangmei Lei

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theore...

Authors: Shrideh Khalaf Al-Omari

Dynamical system of the growth of COVID-19 with controller

Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is bas...

Authors: Rabha W. Ibrahim, Dania Altulea and Rafida M. Elobaid

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second \(q^{b}\)-derivatives

Authors: Muhammad Aamir Ali, Hüseyin Budak, Mujahid Abbas and Yu-Ming Chu

An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

Authors: Li-Bin Liu, Ying Liang, Xiaobing Bao and Honglin Fang

A fractional complex network model for novel corona virus in China

As is well known the novel coronavirus (COVID-19) is a zoonotic virus and our model is concerned with the effect of the zoonotic source of the coronavirus during the outbreak in China. We present a SEIS comple...

Authors: H. A. A. El-Saka, I. Obaya and H. N. Agiza

Novel finite point approach for solving time-fractional convection-dominated diffusion equations

In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point met...

Authors: Xiaomin Liu, Muhammad Abbas, Honghong Yang, Xinqiang Qin and Tahir Nazir

Oscillation of nonlinear third-order difference equations with mixed neutral terms

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformati...

Authors: Jehad Alzabut, Martin Bohner and Said R. Grace

Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis

In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions o...

Authors: Rubayyi T. Alqahtani