Articles

Numerical simulation for fractional-order differential system of a Glioblastoma Multiforme and Immune system

In this paper, we present a numerical simulation to study a fractional-order differential system of a glioblastoma multiforme and immune system. This numerical simulation is based on spectral collocation metho...

Authors: M. M. Al-Shomrani and M. A. Abdelkawy

Green–Haar wavelets method for generalized fractional differential equations

The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of genera...

Authors: Mujeeb ur Rehman, Dumitru Baleanu, Jehad Alzabut, Muhammad Ismail and Umer Saeed

Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a gener...

Authors: Changtong Li, Sanyi Tang and Robert A. Cheke

A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations

In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time,...

Authors: Ben Wongsaijai, Nattakorn Sukantamala and Kanyuta Poochinapan

Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and...

Authors: Yasir Arfat, Poom Kumam, Parinya Sa Ngiamsunthorn, Muhammad Aqeel Ahmad Khan, Hammad Sarwar and Hafiz Fukhar-ud-Din

Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity

In this work, a time-fractional diffusion problem with a time-space dependent diffusivity is considered. The solution of such a problem has a weak singularity at the initial time ...

Authors: Na An

Some identities of Lah–Bell polynomials

Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n. Further, as natural extensions of t...

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

Modeling the effects of contact tracing on COVID-19 transmission

Authors: Ali Traoré and Fourtoua Victorien Konané

Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

Authors: Saad Ihsan Butt, Artion Kashuri, Muhammad Tariq, Jamshed Nasir, Adnan Aslam and Wei Gao

Fractional inclusions of the Hermite–Hadamard type for m-polynomial convex interval-valued functions

Authors: Eze R. Nwaeze, Muhammad Adil Khan and Yu-Ming Chu

Fractional order of Legendre-type matrix polynomials

Recently, special functions of fractional order calculus have had many applications in various areas of mathematical analysis, physics, probability theory, optimization theory, graph theory, control systems, e...

Authors: M. Zayed, M. Hidan, M. Abdalla and M. Abul-Ez

Design of nonstandard computational method for stochastic susceptible–infected–treated–recovered dynamics of coronavirus model

The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear sto...

Authors: Wasfi Shatanawi, Ali Raza, Muhammad Shoaib Arif, Kamaledin Abodayeh, Muhammad Rafiq and Mairaj Bibi

Sinc-Galerkin method for solving the time fractional convection–diffusion equation with variable coefficients

In this paper, a new numerical algorithm for solving the time fractional convection–diffusion equation with variable coefficients is proposed. The time fractional derivative is estimated using the

Authors: Li Juan Chen, MingZhu Li and Qiang Xu

A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for...

Authors: Ahmadreza Haghighi and Roveida Ziaratban

Stochastic SIRC epidemic model with time-delay for COVID-19

Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIR...

Authors: F. A. Rihan, H. J. Alsakaji and C. Rajivganthi

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities ...

Authors: Saad Ihsan Butt, Mehroz Nadeem, Shahid Qaisar, Ahmet Ocak Akdemir and Thabet Abdeljawad

δ-β-Gabor integral operators for a space of locally integrable generalized functions

In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a ...

Authors: Shrideh Khalaf Al-Omari, Dumitru Baleanu and Kottakkaran Sooppy Nisar

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. W...

Authors: Ihsan Ullah, Saeed Ahmad, Qasem Al-Mdallal, Zareen A. Khan, Hasib Khan and Aziz Khan

On high-order compact schemes for the multidimensional time-fractional Schrödinger equation

In this article, some high-order compact finite difference schemes are presented and analyzed to numerically solve one- and two-dimensional time fractional Schrödinger equations. The time Caputo fractional der...

Authors: Rena Eskar, Xinlong Feng and Ehmet Kasim

Generating functions for some families of the generalized Al-Salam–Carlitz q-polynomials

Authors: Hari Mohan Srivastava and Sama Arjika

Exact schemes for second-order linear differential equations in self-adjoint cases

When working with mathematical models, to keep the model errors as small as possible, a special system of linear equations is constructed whose solution vector yields accurate discretized values for the exact ...

Authors: Zoltan Vizvari, Zoltan Sari, Mihaly Klincsik and Peter Odry

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish...

Authors: Thabet Abdeljawad, Saima Rashid, Zakia Hammouch, İmdat İşcan and Yu-Ming Chu

Existence of solutions for subquadratic convex operator equations at resonance and applications to Hamiltonian systems

This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong a...

Authors: Mingliang Song and Ping Chen

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented...

Authors: Khalid K. Ali, Mohamed A. Abd El Salam, Emad M. H. Mohamed, Bessem Samet, Sunil Kumar and M. S. Osman

Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global posit...

Authors: Suxia Wang, Juan Zhao, Junxing Zhu and Xiaoli Ren

Computation of certain integral formulas involving generalized Wright function

The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms ...

Authors: Nabiullah Khan, Talha Usman, Mohd Aman, Shrideh Al-Omari and Serkan Araci

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibri...

Authors: Shahram Rezapour, Hakimeh Mohammadi and Mohammad Esmael Samei

Modeling and forecasting the spread tendency of the COVID-19 in China

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on col...

Authors: Deshun Sun, Li Duan, Jianyi Xiong and Daping Wang

A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stabil...

Authors: Shahram Rezapour and Hakimeh Mohammadi

On modeling of coronavirus-19 disease under Mittag-Leffler power law

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivat...

Authors: Samia Bushnaq, Kamal Shah and Hussam Alrabaiah

Note on some representations of general solutions to homogeneous linear difference equations

Authors: Stevo Stević, Bratislav Iričanin, Witold Kosmala and Zdeněk Šmarda

An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive ...

Authors: Monairah Alansari, Mohammad Farid and Rehan Ali

Curved fronts of bistable reaction–diffusion equations with nonlinear convection

This paper is concerned with traveling curved fronts of bistable reaction–diffusion equations with nonlinear convection in a two-dimensional space. By constructing super- and subsolutions, we establish the exi...

Authors: Hui-Ling Niu and Jiayin Liu

An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equati...

Authors: Amar Deep, Deepmala, Jamal Rezaei Roshan, Kottakkaran Sooppy Nisar and Thabet Abdeljawad

Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschi...

Authors: Yousef Gholami

A mathematical analysis of a system of Caputo–Fabrizio fractional differential equations for the anthrax disease model in animals

We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional

Authors: Shahram Rezapour, Sina Etemad and Hakimeh Mohammadi

Uniqueness of meromorphic functions concerning their difference operators and derivatives

Let f and g be two nonconstant meromorphic functions. Shared value problems related to f and g are investigated in this paper. We give sufficient conditions in terms of weighted value sharing which imply that f i...

Authors: Dong-Mei Wei and Zhi-Gang Huang

Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model

In this paper, a fast collocation method is developed for a two-dimensional variable-coefficient linear nonlocal diffusion model. By carefully dealing with the variable coefficient in the integral operator and...

Authors: Xuhao Zhang and Aijie Cheng

New finite-time synchronization analysis of a delayed memristive neurodynamic model

This paper presents theoretical results on the finite-time synchronization of delayed memristive neural networks (MNNs). Compared with existing ones on finite-time synchronization of discontinuous NNs, we dire...

Authors: Dandan Ren and Aidi Yao

Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equat...

Authors: Idris Ahmed, Poom Kumam, Jamilu Abubakar, Piyachat Borisut and Kanokwan Sitthithakerngkiet

Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computat...

Authors: Abdel-Haleem Abdel-Aty, Mostafa M. A. Khater, Dumitru Baleanu, E. M. Khalil, Jamel Bouslimi and M. Omri

Existence of nonoscillatory solutions to nonlinear higher-order neutral dynamic equations

We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of...

Authors: Yang-Cong Qiu, Kuo-Shou Chiu, Irena Jadlovská and Tongxing Li

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gauss...

Authors: Huihong Zhao, Zhifang Li, Bin Li and Tongxing Li

On a Caputo conformable inclusion problem with mixed Riemann–Liouville conformable integro-derivative conditions

We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In t...

Authors: Dumitru Baleanu, Sina Etemad and Shahram Rezapour

Fuzzy fractional-order model of the novel coronavirus

In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo’s sense is developed. By using the fuzzy Laplace method coupled with Adomian decomposition tr...

Authors: S. Ahmad, A. Ullah, K. Shah, S. Salahshour, A. Ahmadian and T. Ciano

A generalized isospectral–nonisospectral heat equation hierarchy and its expanding integrable model

A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usu...

Authors: Huanhuan Lu, Yufeng Zhang and Jianqin Mei

Existence and uniqueness of solutions for coupled system of fractional differential equations involving proportional delay by means of topological degree theory

In this manuscript, we obtain sufficient conditions required for the existence of solution to the following coupled system of nonlinear fractional order differential equations:

Authors: Anwar Ali, Muhammad Sarwar, Mian Bahadur Zada and Thabet Abdeljawad

Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment

Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquit...

Authors: Ting-Ting Zheng, Lin-Fei Nie, Zhidong Teng and Yantao Luo

Analytical properties of the Hurwitz–Lerch zeta function

Authors: Raghib Nadeem, Talha Usman, Kottakkaran Sooppy Nisar and Dumitru Baleanu

New generating functions of I-function satisfying Truesdell’s \(F_{q}\)-equation

Authors: Altaf Ahmad Bhat, Asifa Tassaddiq, D. K. Jain and Humera Naaz