Articles

Mathematical modeling of hepatitis B virus infection for antiviral therapy using LHAM

Anti-viral therapy is comparatively very effective for patients who get affected by the hepatitis B virus. It is of prime importance to understand the different relations among the viruses, immune responses an...

Authors: M. Aniji, N. Kavitha and S. Balamuralitharan

On existence and stability results to a class of boundary value problems under Mittag-Leffler power law

Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are establish...

Authors: Gauhar Ali, Kamal Shah, Thabet Abdeljawad, Hasib Khan, Ghaus Ur Rahman and Aziz Khan

Some new local fractional inequalities associated with generalized \((s,m)\)-convex functions and applications

Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attract...

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

Corrosion shape reconstruction of the mixed boundary in electrostatic imaging

We consider the corrosion detection problem in terms of the Laplace equation and study a simply connected bounded domain with Wentzell-type GIBC boundary condition. We derive the systems of integral equations ...

Authors: Yuqing Hu, Bingxian Wang and Tongxing Li

Hyers–Ulam stability of linear fractional differential equations with variable coefficients

Motivated by Shen et al., we apply the Gronwall’s inequality to establish the Hyers–Ulam stability of two types (Riemann–Liouville and Caputo) of linear fractional differential equations with variable coeffici...

Authors: Hui Liu and Yongjin Li

Estimates of certain paraxial diffraction integral operator and its generalized properties

This paper aims to discuss a generalization of certain paraxial diffraction integral operator in a class of generalized functions. At the start of this paper, we propose a convolution formula and establish cer...

Authors: Shrideh Al-Omari, Serkan Araci, Mohammed Al-Smadi, Ghaleb Gumah and Hussam Alrabaiah

Some reverse inequalities of Hardy type on time scales

In this article, we obtain some new dynamic inequalities of Hardy type on time scales. The main results are derived using Fubini’s theorem and the chain rule on time scales. We apply the main results to the co...

Authors: A. A. El-Deeb, H. A. El-Sennary and Zareen A. Khan

Modelling intracellular delay and therapy interruptions within Ghanaian HIV population

This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an...

Authors: Kofi F. Owusu, Emile F. Doungmo Goufo and Stella Mugisha

Stability analysis of a diagonally implicit scheme of block backward differentiation formula for stiff pharmacokinetics models

In this paper, we analyze the criteria for the stability of a method suited to the ordinary differential equations models. The relevant proof that the method satisfies the condition of stiff stability is also ...

Authors: Hazizah Mohd Ijam, Zarina Bibi Ibrahim, Zanariah Abdul Majid and Norazak Senu

Influence of impreciseness in designing tritrophic level complex food chain modeling in interval environment

In this paper, we construct a tritrophic level food chain model considering the model parameters as fuzzy interval numbers. We check the positivity and boundedness of solutions of the model system and find out...

Authors: Animesh Mahata, Sankar Prasad Mondal, Banamali Roy, Shariful Alam, Mehdi Salimi, Ali Ahmadian and Massimiliano Ferrara

A GPIU method for fractional diffusion equations

The fractional diffusion equations can be discretized by applying the implicit finite difference scheme and the unconditionally stable shifted Grünwald formula. Hence, the generating linear system has a real T...

Authors: Hai-Long Shen, Yu-Han Li and Xin-Hui Shao

Stability and bifurcation analysis of two-species competitive model with Michaelis–Menten type harvesting in the first species

In this paper, a two-species competitive model with Michaelis–Menten type harvesting in the first species is studied. We have made a detailed mathematical analysis of the model to describe some important resul...

Authors: Xiangqin Yu, Zhenliang Zhu and Zhong Li

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line

In this paper we consider a fractional differential system with coupled integral boundary value problems on a half-line, where the nonlinearity terms depend on unknown functions and the lower-order fractional ...

Authors: Haiyan Zhang, Yongqing Wang and Jiafa Xu

Local stability of mappings on multi-normed spaces

First we investigate the Hyers–Ulam stability of the Cauchy functional equation for mappings from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equa...

Authors: Choonkil Park, Batool Noori, M. B. Moghimi, Abbas Najati and J. M. Rassias

Analysis of Caputo fractional-order model for COVID-19 with lockdown

One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a m...

Authors: Idris Ahmed, Isa Abdullahi Baba, Abdullahi Yusuf, Poom Kumam and Wiyada Kumam

Approximation by Jakimovski–Leviatan-beta operators in weighted space

The main purpose of this article is to introduce a more generalized version of Jakimovski–Leviatan-beta operators through the Appell polynomials. We present some uniform convergence results of these operators ...

Authors: M. Nasiruzzaman and M. Mursaleen

A note on degenerate poly-Genocchi numbers and polynomials

Recently, some mathematicians have been studying a lot of degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our research is also interested in this field. In ...

Authors: Hye Kyung Kim and Lee-Chae Jang

New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system

According to the report presented by the World Health Organization, a new member of viruses, namely, coronavirus, shortly 2019-nCoV, which arised in Wuhan, China, on January 7, 2020, has been introduced to the...

Authors: Wei Gao, Haci Mehmet Baskonus and Li Shi

Solving the Riesz–Feller space-fractional backward diffusion problem by a generalized Tikhonov method

The article investigates a Riesz–Feller space-fractional backward diffusion problem. We develop a generalized Tikhonov regularization method to overcome the ill-posedness of this problem, and then based on the...

Authors: Hongwu Zhang and Xiaoju Zhang

Mittag-Leffler–Hyers–Ulam stability of differential equation using Fourier transform

This research paper aims to present the results on the Mittag-Leffler–Hyers–Ulam and Mittag-Leffler–Hyers–Ulam–Rassias stability of linear differential equations of first, second, and nth order by the Fourier tra...

Authors: Arusamy Mohanapriya, Choonkil Park, Anumanthappa Ganesh and Vediyappan Govindan

Novel finite-time synchronization criteria for coupled network systems with time-varying delays via event-triggered control

This paper is concerned with the finite-time synchronization of coupled networks with time-varying delays. We work without applying the finite-time stability theorem, which is widely used in finite-time synchr...

Authors: Wenxia Cui, Wenbin Jin and Zhenjie Wang

Oscillatory behavior of second-order nonlinear neutral differential equations

We shall consider a class of second-order nonlinear neutral differential equations. Some new oscillation criteria are established by using the Riccati transformation technique. One example is given to show the...

Authors: Jun Liu, Xi Liu and Yuanhong Yu

Stochastic patch structure Nicholson’s blowflies system with mixed delays

This paper is devoted to studying a stochastic patch structure Nicholson’s blowflies system with mixed delays which is a new model for the generalization of classic Nicholson’s blowflies system. We examine sto...

Authors: Honghui Yin, Bo Du and Xiwang Cheng

Two sequential fractional hybrid differential inclusions

The main objective of this paper is to concern with a new category of the sequential hybrid inclusion boundary value problem with three-point integro-derivative boundary conditions. In this direction, we emplo...

Authors: Hakimeh Mohammadi, Shahram Rezapour, Sina Etemad and Dumitru Baleanu

Existence of solution and stability for the fractional order novel coronavirus (nCoV-2019) model

The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo–Fabrizio derivative. We make use of fixed point theory and Picard–Lindelöf technique to explore the...

Authors: Azhar Hussain, Dumitru Baleanu and Muhammad Adeel

New quantum estimates in the setting of fractional calculus theory

Authors: Saima Rashid, Zakia Hammouch, Rehana Ashraf, Dumitru Baleanu and Kottakkaran Sooppy Nisar

On the mathematical model of Rabies by using the fractional Caputo–Fabrizio derivative

Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate t...

Authors: Seher Melike Aydogan, Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control

This paper concerns a kind of stochastic optimal control problem with recursive utility described by a reflected backward stochastic differential equation (RBSDE, for short) involving diffusion type control wh...

Authors: Zhenda Xu

Reconstruction of nonlinear integral inequalities associated with time scales calculus

In this paper, we build up some generalizations of nonlinear integral inequalities and recreate the results of some Pachpatte’s inequalities on time scales. We not just settle new estimated bounds of a particu...

Authors: Zareen A. Khan

Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism

This paper is related to some dynamical aspects of a class of predator–prey interactions incorporating cannibalism and Allee effects for non-overlapping generations. Cannibalism has been frequently observed in...

Authors: Muhammad Sajjad Shabbir, Qamar Din, Khalil Ahmad, Asifa Tassaddiq, Atif Hassan Soori and Muhammad Asif Khan

Nonparametric threshold estimation of spot volatility based on high-frequency data for time-dependent diffusion models with jumps

We construct a spot volatility kernel estimator of time-dependent diffusion models with jumps. Instead of idiomatic intraday return over an observation interval, in the proposed estimator, we use intraday rang...

Authors: Jingwei Cai, Quanxin Zhu and Ping Chen

Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and bounde...

Authors: Deshun Sun, Lingyun Lu, Fei Liu, Li Duan, Daping Wang and Jianyi Xiong

Improved synchronization criteria for fractional-order complex-valued neural networks via partial control

In this article, without dividing a complex-valued neural network into two real-valued subsystems, the global synchronization of fractional-order complex-valued neural networks (FOCVNNs) is investigated by the...

Authors: Hong-Li Li, Ahmadjan Muhammadhaji, Long Zhang, Haijun Jiang and Zhidong Teng

Laplace decomposition for solving nonlinear system of fractional order partial differential equations

In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in te...

Authors: Hassan Khan, Rasool Shah, Poom Kumam, Dumitru Baleanu and Muhammad Arif

Some modifications in conformable fractional integral inequalities

The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional c...

Authors: Dumitru Baleanu, Pshtiwan Othman Mohammed, Miguel Vivas-Cortez and Yenny Rangel-Oliveros

A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking th...

Authors: Amjad Salim Shaikh, Iqbal Najiroddin Shaikh and Kottakkaran Sooppy Nisar

Adaptive control realization for canonic Caputo fractional-order systems with actuator nonlinearity: application to mechatronic devices

Nonlinearities, such as dead-zone, backlash, hysteresis, and saturation, are common in the mechanical and mechatronic systems’ components and actuators. Hence, an effective control strategy should take into ac...

Authors: Mohammad Pourmahmood Aghababa and Mehrdad Saif

Correction to: A B-spline finite element method for solving a class of nonlinear parabolic equations modeling epitaxial thin-film growth with variable coefficient

In the original publication of this article [1] the name of the second author is incorrect. The correct name of the second author is Jiawei Tan rather than John Jiawei Tan. The error in this Correction has bee...

Authors: Dandan Qin, Jiawei Tan, Bo Liu and Wenzhu Huang

Existence results of fractional delta–nabla difference equations via mixed boundary conditions

In this article, we purpose existence results for a fractional delta–nabla difference equations with mixed boundary conditions by using Banach contraction principle and Schauder’s fixed point theorem. Our prob...

Authors: Jiraporn Reunsumrit and Thanin Sitthiwirattham

Topological degree theory and Caputo–Hadamard fractional boundary value problems

We study two hybrid and non-hybrid fractional boundary value problems via the Caputo–Hadamard type derivatives. We seek the existence criteria for these two problems separately. By utilizing the generalized Dh...

Authors: Abdelkader Amara, Sina Etemad and Shahram Rezapour

On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals

In this paper, we establish the generalized Riemann–Liouville (RL) fractional integrals in the sense of another increasing, positive, monotone, and measurable function Ψ. We determine certain new double-weighted ...

Authors: Gauhar Rahman, Kottakkaran Sooppy Nisar, Behzad Ghanbari and Thabet Abdeljawad

Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel

This paper presents a fundamental solution method for nonlinear fractional regularized long-wave (RLW) models. Since analytical methods cannot be applied easily to solve such models, numerical or semianalytica...

Authors: Mehmet Yavuz and Thabet Abdeljawad

Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters

This paper is concerned with the number of limit cycles bifurcating from a period annulus for some planar piecewise smooth non-Hamiltonian systems. We construct a planar piecewise quadratic system with multipl...

Authors: Shuhua Gong and Maoan Han

Dunkl generalization of Phillips operators and approximation in weighted spaces

Authors: M. Mursaleen, Md. Nasiruzzaman, A. Kılıçman and S. H. Sapar

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

At first, we construct a connection between the Atangana–Baleanu and the Riemann–Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this rela...

Authors: Pshtiwan Othman Mohammed and Thabet Abdeljawad

Certain results on a hybrid class of the Boas–Buck polynomials

This article aims to introduce a hybrid family of 2-variable Boas–Buck-general polynomials by taking Boas–Buck polynomials as a base with the 2-variable general polynomials. These polynomials are framed within...

Authors: Ghazala Yasmin, Hibah Islahi and Abdulghani Muhyi

On a coupled system of fractional sum-difference equations with p-Laplacian operator

In this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both Riemann–Liouv...

Authors: Pimchana Siricharuanun, Saowaluck Chasreechai and Thanin Sitthiwirattham

Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations

In this article, a finite volume element method with the second-order weighted and shifted Grünwald difference (WSGD) formula is proposed and studied for nonlinear time fractional mobile/immobile transport equ...

Authors: Jie Zhao, Zhichao Fang, Hong Li and Yang Liu

Pullback attractors of nonautonomous discrete p-Laplacian complex Ginzburg–Landau equations with fast-varying delays

In this paper, we consider a class of nonautonomous discrete p-Laplacian complex Ginzburg–Landau equations with time-varying delays. We prove the existence and uniqueness of pullback attractor for these equations...

Authors: Xiaoqin Pu, Xuemin Wang and Dingshi Li

Fractional modeling and control in a delayed predator-prey system: extended feedback scheme

This paper’s goal is to delve into the fractional modeling and bifurcation control for a predator-prey model with prey dispersal and gestation delay. First, the bifurcation criteria for the uncontrolled system...

Authors: Shuai Li, Chengdai Huang, Shuli Guo and Xinyu Song