Articles

Optimal consumption and portfolio selection with lower and upper bounds on consumption

We investigate the optimal consumption and investment problem with lower and upper bounds on consumption constraints. We derive closed-form solutions by means of the dynamic programming approach. We also evalu...

Authors: Kum-Hwan Roh and Yong Hyun Shin

Existence results of nonlocal Robin boundary value problems for fractional \((p,q)\)-integrodifference equations

Authors: Jarunee Soontharanon and Thanin Sitthiwirattham

Stability and bifurcation analysis of an amensalism system with Allee effect

In this work, we propose and study a new amensalism system with Allee effect on the first species. First, we investigate the existence and stability of all possible coexistence equilibrium points and boundary ...

Authors: Ming Zhao and Yunfei Du

Theoretical analysis of the delay on the p53 micronetwork

Time delay plays a crucial role in p53 dynamic. However, the theoretical understanding is still lower. Thus we construct a micro-differential equation model and introduce the time delay τ based on the regulation ...

Authors: Danni Wang, Nan Liu, Hongli Yang and Liangui Yang

Ulam–Hyers–Rassias stability for nonlinear Ψ-Hilfer stochastic fractional differential equation with uncertainty

We consider a nonlinear Cauchy problem involving the Ψ-Hilfer stochastic fractional derivative with uncertainty, and we give a stability result. Using fixed point theory, we are able to provide a fuzzy Ulam–Hyers...

Authors: Reza Chaharpashlou, Reza Saadati and Abdon Atangana

Solvability and stability of a fractional dynamical system of the growth of COVID-19 with approximate solution by fractional Chebyshev polynomials

Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a sys...

Authors: Samir B. Hadid, Rabha W. Ibrahim, Dania Altulea and Shaher Momani

The controllability of damped fractional differential system with impulses and state delay

We discuss the controllability for a damped fractional differential system with impulses and state delay, which involves Caputo fractional derivatives. Deriving the condition based on the Gramian matrix define...

Authors: Musarrat Nawaz, Jiang Wei, Jiale Sheng and Azmat Ullaha Khan

An extension of several essential numerical radius inequalities of \(2\times 2\) off-diagonal operator matrices

Authors: Mohammed Al-Dolat, Imad Jaradat and Dumitru Baleanu

Growth of solutions for a coupled nonlinear Klein–Gordon system with strong damping, source, and distributed delay terms

In this work, the exponential growth of solutions for a coupled nonlinear Klein–Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions.

Authors: Abdelaziz Rahmoune, Djamel Ouchenane, Salah Boulaaras and Praveen Agarwal

Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative

In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined by a system of eighteen fractional differential equations. ...

Authors: Nasser Hassan Sweilam, Seham Mahyoub Al-Mekhlafi, Taghreed Assiri and Abdon Atangana

A new bound for the Jensen gap pertaining twice differentiable functions with applications

In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the ...

Authors: Shahid Khan, Muhammad Adil Khan, Saad Ihsan Butt and Yu-Ming Chu

Synchronization of bidirection multiple neural networks with impulsive coupling control

This paper is devoted to the study of the global synchronization of multiple neural networks (MNNs) via impulsive coupling control. Compared to one-layer neural networks, MNNs have more complex dynamics behavi...

Authors: Yong Wang, Ailong Wu and Biwen Li

A detailed study on a new \((2 + 1)\)-dimensional mKdV equation involving the Caputo–Fabrizio time-fractional derivative

Authors: K. Hosseini, M. Ilie, M. Mirzazadeh and D. Baleanu

On new fractional integral inequalities for p-convexity within interval-valued functions

This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integ...

Authors: Thabet Abdeljawad, Saima Rashid, Hasib Khan and Yu-Ming Chu

On Hilfer generalized proportional fractional derivative

Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo ...

Authors: Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut and Wachirapong Jirakitpuwapat

Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method

The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical a...

Authors: Behzad Ghanbari, Kottakkaran Sooppy Nisar and Mujahed Aldhaifallah

Comparison of fuzzy Adomian decomposition method with fuzzy VIM for solving fuzzy heat-like and wave-like equations with variable coefficients

In this work, we investigate the fuzzy Adomian decomposition method (ADM) and fuzzy variational iteration method (VIM) applied to solving fuzzy heat-like and wave-like equations with variable coefficients, in ...

Authors: Mawia Osman, Zengtai Gong and Altyeb Mohammed Mustafa

\(C^{*}\)-Algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation

Authors: R. Chaharpashlou, Donal O’Regan, Choonkil Park and Reza Saadati

On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric funct...

Authors: Rabha W. Ibrahim, Rafida M. Elobaid and Suzan J. Obaiys

Gradient-descent iterative algorithm for solving a class of linear matrix equations with applications to heat and Poisson equations

Authors: Adisorn Kittisopaporn and Pattrawut Chansangiam

Study of transmission dynamics of novel COVID-19 by using mathematical model

In this research work, we present a mathematical model for novel coronavirus-19 infectious disease which consists of three different compartments: susceptible, infected, and recovered under convex incident rat...

Authors: Rahim Ud Din, Kamal Shah, Imtiaz Ahmad and Thabet Abdeljawad

Stochastic Hopf–Hopf bifurcation of two-species discrete coupling logistic system with symbiotic interaction

In this paper, stochastic Hopf–Hopf bifurcation of the discrete coupling logistic system with symbiotic interaction is investigated. Firstly, orthogonal polynomial approximation of discrete random function in ...

Authors: Maosong Yang and Shaojuan Ma

Modeling the Allee effect and fear effect in predator–prey system incorporating a prey refuge

In this paper, we consider a predator–prey model with Allee effect, fear effect and prey refuge. By considering the prey refuge as a parameter, we give the threshold condition for the stability of the system, ...

Authors: Ying Huang, Zhenliang Zhu and Zhong Li

Impact of Michaelis–Menten type harvesting in a Lotka–Volterra predator–prey system incorporating fear effect

We propose and study a Lotka–Volterra predator–prey system incorporating both Michaelis–Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study t...

Authors: Liyun Lai, Xiangqin Yu, Mengxin He and Zhong Li

A new approach to interval-valued inequalities

The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate s...

Authors: Awais Younus, Muhammad Asif, Jehad Alzabut, Abdul Ghaffar and Kottakkaran Sooppy Nisar

Dynamic of interactive model for information propagation across social networks media

Controlling information diffusion or propagation through social networks can be challenging when dealing with information related to a subject of highest interest for the public. The complexity level of contro...

Authors: Yaming Zhang, Fei Liu, Yaya H. Koura and Hao Wang

Approximation of functions in generalized Zygmund class by double Hausdorff matrix

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

Existence and Ulam stability results of a coupled system for terminal value problems involving ψ-Hilfer fractional operator

The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at ha...

Authors: Mohammed S. Abdo, Kamal Shah, Satish K. Panchal and Hanan A. Wahash

Numerical solution for the time-fractional Fokker–Planck equation via shifted Chebyshev polynomials of the fourth kind

This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to presen...

Authors: Haile Habenom and D. L. Suthar

Oscillation of solutions of third order nonlinear neutral differential equations

Authors: Ragaa A. Sallam, Shaimaa Salem and Mohamed M. A. El-Sheikh

Modified Chebyshev collocation method for delayed predator–prey system

In this study, the approximate solutions of the predator–prey system with delay have been obtained by using the modified Chebyshev collocation method. The main technique is that this method transforms the orig...

Authors: J. Dengata and Shufang Ma

Event-triggered sampled-data synchronization of complex networks with time-varying coupling delays

This paper investigates the event-triggered sampled-data synchronization problem of complex networks with time-varying coupling delays. The sampled-data controller is designed with event-triggered mechanisms. ...

Authors: Yang Yang and Yue Long

Some results on degenerate Daehee and Bernoulli numbers and polynomials

In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually called the degenerate Daehee polynomials and number...

Authors: Taekyun Kim, Dae San Kim, Han Young Kim and Jongkyum Kwon

Blow up of solutions of two singular nonlinear viscoelastic equations with general source and localized frictional damping terms

This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. This work is...

Authors: Salah Boulaaras, Abdelbaki Choucha, Djamel Ouchenane and Bahri Cherif

Hexagonal grid approximation of the solution of the heat equation on special polygons

Authors: Suzan C. Buranay and Nouman Arshad

A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order

Authors: Abdul Ghaffar, Ayyaz Ali, Sarfaraz Ahmed, Saima Akram, Moin-ud-Din Junjua, Dumitru Baleanu and Kottakkaran Sooppy Nisar

Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms

This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-l...

Authors: G. Chen, A. Lastra and S. Malek

Existence of infinitely many high energy solutions for a class of fractional Schrödinger systems

Authors: Qi Li, Zengqin Zhao and Xinsheng Du

Natural convection flow of a fluid using Atangana and Baleanu fractional model

A modified fractional model for the magnetohydrodynamic (MHD) flow of a fluid is developed utilizing Atangana–Baleanu fractional derivative (ABFD). Natural convection and wall oscillation instigate the flow ov...

Authors: Sidra Aman, Thabet Abdeljawad and Qasem Al-Mdallal

Solutions of two fractional q-integro-differential equations under sum and integral boundary value conditions on a time scale

Authors: Jehad Alzabut, Behnam Mohammadaliee and Mohammad Esmael Samei

More properties of the proportional fractional integrals and derivatives of a function with respect to another function

In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the...

Authors: Fahd Jarad, Thabet Abdeljawad, Saima Rashid and Zakia Hammouch

On a hybrid inclusion problem via hybrid boundary value conditions

In this manuscript, the existence of solutions for a novel category of the fractional differential equation of hybrid type with hybrid boundary value conditions is studied. Also, we review the existence result...

Authors: S. Etemad, S. Pourrazi and Sh. Rezapour

On a fractional hybrid version of the Sturm–Liouville equation

It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible...

Authors: Zohreh Zeinalabedini Charandabi, Shahram Rezapour and Mina Ettefagh

On stability analysis and existence of positive solutions for a general non-linear fractional differential equations

In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Lap...

Authors: Amita Devi, Anoop Kumar, Dumitru Baleanu and Aziz Khan

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplac...

Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

The r-central factorial numbers with even indices

In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several ...

Authors: F. A. Shiha

On a unified integral operator for φ-convex functions

Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bou...

Authors: Young Chel Kwun, Moquddsa Zahra, Ghulam Farid, Saira Zainab and Shin Min Kang

Existence of solutions for an ordinary second-order hybrid functional differential equation

In this paper, we study the existence of solutions for an initial value problem of an ordinary second-order hybrid functional differential equation (SHDE) using a fixed point theorem of Dhage. Example is given...

Authors: Ahmed El-Sayed, Hind Hashem and Shorouk Al-Issa

Positive solutions for a system of Riemann–Liouville fractional boundary value problems with p-Laplacian operators

We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p-Laplacian operators, nonnegative nonlinearities and positive parameters, su...

Authors: Alexandru Tudorache and Rodica Luca

Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method

In this paper, we present a numerical method to solve two-dimensional fuzzy Fredholm integral equations (2D-FFIE) by combing the sinc method with double exponential (DE) transformation. Using this method, the ...

Authors: Yanying Ma, Hu Li and Suping Zhang