Articles

Finite-time stability of linear stochastic fractional-order systems with time delay

Authors: Lassaad Mchiri, Abdellatif Ben Makhlouf, Dumitru Baleanu and Mohamed Rhaima

Dynamical analysis of a stochastic three-species predator–prey system with distributed delays

A stochastic two-prey one-predator system with distributed delays is proposed in this paper. Firstly, applying the linear chain technique, we transform the predator–prey system with distributed delays to an eq...

Authors: Jinxing Zhao and Yuanfu Shao

A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves R...

Authors: Ahmed Nouara, Abdelkader Amara, Eva Kaslik, Sina Etemad, Shahram Rezapour, Francisco Martinez and Mohammed K. A. Kaabar

Study on new integral operators defined using confluent hypergeometric function

Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preser...

Authors: Georgia Irina Oros

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data ...

Authors: Pushpendra Kumar, Vedat Suat Erturk, Marina Murillo-Arcila, Ramashis Banerjee and A. Manickam

Mathematical modeling of non-Newtonian fluid in arterial blood flow through various stenoses

Since the stenosis geometry of some cardiovascular patients cannot be described by a vertically symmetric function throughout the stenosis, so it motivates us to study the blood flow through a vertically asymm...

Authors: Pinyo Owasit and Somchai Sriyab

Fixed point theory in the setting of \((\alpha,\beta,\psi,\phi)\)-interpolative contractions

Authors: Erdal Karapınar, Andreea Fulga and Antonio Francisco Roldán López de Hierro

The dynamics of a Leslie type predator–prey model with fear and Allee effect

In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account...

Authors: S. Vinoth, R. Sivasamy, K. Sathiyanathan, Bundit Unyong, Grienggrai Rajchakit, R. Vadivel and Nallappan Gunasekaran

An SEIR model with infected immigrants and recovered emigrants

We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local pop...

Authors: Peter J. Witbooi

A new structure of an integral operator associated with trigonometric Dunkl settings

In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolut...

Authors: Shrideh Khalaf Al-Omari, Serkan Araci and Mohammed Al-Smadi

Correction to: A study of symmetric contractions with an application to generalized fractional differential equations

Authors: Aftab Hussain, Fahd Jarad and Erdal Karapinar

New coincidence point results for generalized graph-preserving multivalued mappings with applications

This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms). An example and some corollaries are deriv...

Authors: Hasanen A. Hammad, Manuel De la Sen and Praveen Agarwal

Some trapezoid and midpoint type inequalities via fractional \((p,q)\)-calculus

Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of resear...

Authors: Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Praveen Agarwal

Closed-form pricing formula for foreign equity option with credit risk

Since credit risk in the over-the-counter (OTC) market has undoubtedly become very important issue, credit risk has to be considered when the options in the OTC market are priced. In this paper, we consider th...

Authors: Donghyun Kim, Ji-Hun Yoon and Geonwoo Kim

Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations

In this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given conditions is introduced. The collocation method is used with ratio...

Authors: Mohamed A. Abd El Salam, Mohamed A. Ramadan, Mahmoud A. Nassar, Praveen Agarwal and Yu-Ming Chu

Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

In this paper, we prove two results concerning the existence of S-asymptotically ω-periodic solutions for non-instantaneous impulsive semilinear differential inclusions of order ...

Authors: Zainab Alsheekhhussain, JinRong Wang and Ahmed Gamal Ibrahim

Generalized homogeneous q-difference equations for q-polynomials and their applications to generating functions and fractional q-integrals

In this paper, our aim is to build generalized homogeneous q-difference equations for q-polynomials. We also consider their applications to generating functions and fractional q-integrals by using the perspective...

Authors: Jian Cao, Hong-Li Zhou and Sama Arjika

Common fixed point theorem on Proinov type mappings via simulation function

In this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. W...

Authors: Badr Alqahtani, Sara Salem Alzaid, Andreea Fulga and Seher Sultan Yeşilkaya

Analytical solution of non-linear fractional diffusion equation

In this paper, we obtain an approximate/analytical solution of nonlinear fractional diffusion equation using the q-homotopy analysis transform method. The existence and uniqueness of the solution for this prob...

Authors: Obaid Alqahtani

Some new formulas of complete and incomplete degenerate Bell polynomials

The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and incomplete Bell polynomials, and to derive some properties and ident...

Authors: Dae San Kim, Taekyun Kim, Si-Hyeon Lee and Jin-Woo Park

Analysis of fractional differential equations with fractional derivative of generalized Mittag-Leffler kernel

In this paper, we study classes of linear and nonlinear multi-term fractional differential equations involving a fractional derivative with generalized Mittag-Leffler kernel. Estimates of fractional derivative...

Authors: Mohammed Al-Refai, Abdalla Aljarrah and Thabet Abdeljawad

On a fractional problem of Lane–Emden type: Ulam type stabilities and numerical behaviors

In this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane–Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivat...

Authors: Kamel Tablennehas, Zoubir Dahmani, Meriem Mansouria Belhamiti, Amira Abdelnebi and Mehmet Zeki Sarikaya

On partial fractional Sturm–Liouville equation and inclusion

The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville...

Authors: Zohreh Zeinalabedini Charandabi, Hakimeh Mohammadi, Shahram Rezapour and Hashem Parvaneh Masiha

Lie symmetry and μ-symmetry methods for nonlinear generalized Camassa–Holm equation

In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as a result reduction of the order and computing the conservation laws are presented. Furthermore, μ-symmetry a...

Authors: H. Jafari, K. Goodarzi, M. Khorshidi, V. Parvaneh and Z. Hammouch

Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative

In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence ...

Authors: Hojjat Afshari, Hossein Hosseinpour and H. R. Marasi

Time-delay effect on a diffusive predator–prey model with habitat complexity

Based on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. Firstly, the stability of the equilibr...

Authors: Yanfeng Li, Haicheng Liu and Ruizhi Yang

Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator wit...

Authors: F. Talay Akyildiz and Fehaid Salem Alshammari

Second-order impulsive differential systems with mixed and several delays

In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and ...

Authors: Shyam Sundar Santra, Apurba Ghosh, Omar Bazighifan, Khaled Mohamed Khedher and Taher A. Nofal

Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

In this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the...

Authors: Raheel Kamal, Kamran, Gul Rahmat, Ali Ahmadian, Noreen Izza Arshad and Soheil Salahshour

Blowup for nonlinearly damped viscoelastic equations with logarithmic source and delay terms

In this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to the nonlinear damping term instead of strong ...

Authors: Sun-Hye Park

Event-triggered H-infinity finite-time consensus control for nonlinear second-order multi-agent systems with disturbances

The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the...

Authors: Yiping Luo and Wanling Zhu

Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order

In this contribution, we investigate an initial-boundary value problem for a fractional diffusion equation with Caputo fractional derivative of space-dependent variable order where the coefficients are depende...

Authors: Karel Van Bockstal

Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative

Authors: Zhilin Yang

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some gener...

Authors: Hüseyin Budak, Fatih Hezenci and Hasan Kara

Unified multivalued interpolative Reich–Rus–Ćirić-type contractions

This article examines new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions and fixed point results for multivalued maps that fulfill these conditions. Earlier defined interpolative contrac...

Authors: Monairah Alansari and Muhammad Usman Ali

Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

The objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued ...

Authors: Abdullah Shoaib, Qasim Mahmood, Aqeel Shahzad, Mohd Salmi Md Noorani and Stojan Radenović

Existence of solutions for a coupled system of fractional differential equations by means of topological degree theory

This paper investigates the existence of solutions for a coupled system of fractional differential equations. The existence is proved by using the topological degree theory, and an example is given to show the...

Authors: Jingli Xie and Lijing Duan

A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system

The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study t...

Authors: Dumitru Baleanu, Sadegh Zibaei, Mehran Namjoo and Amin Jajarmi

Stable finite difference method for fractional reaction–diffusion equations by compact implicit integration factor methods

In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in a two-dimensional domain. The space discretization is implemented by the weighted shifted Grünwa...

Authors: Rongpei Zhang, Mingjun Li, Bo Chen and Liwei Zhang

Common fixed point theorems on quasi-cone metric space over a divisible Banach algebra

In this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-mappings defined on quasi-cone metric space over a divisible Banach algebra via an auxiliary mapping ϕ.

Authors: Andreea Fulga, Hojjat Afshari and Hadi Shojaat

Some new Opial type dynamic inequalities via convex functions and applications

In this paper, we prove some new Opial-type dynamic inequalities on time scales. Our results are obtained in frame of convexity property and by using the chain rule and Jensen and Hölder inequalities. For illu...

Authors: S. H. Saker, J. Alzabut, A. G. Sayed and D. O’Regan

Some properties of degenerate complete and partial Bell polynomials

In this paper, we study degenerate complete and partial Bell polynomials and establish some new identities for those polynomials. In addition, we investigate the connections between modified degenerate complet...

Authors: Taekyun Kim, Dae San Kim, Jongkyum Kwon, Hyunseok Lee and Seong-Ho Park

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the resu...

Authors: Maryam Aleem, Mujeeb Ur Rehman, Jehad Alzabut, Sina Etemad and Shahram Rezapour

Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

In this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competen...

Authors: Denghao Pang, Wei Jiang, Azmat Ullah Khan Niazi and Jiale Sheng

Lower and upper solutions method to the fully elastic cantilever beam equation with support

The aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected to a resilient supporting device, that is,

Authors: Mei Wei, Yongxiang Li and Gang Li

A study of symmetric contractions with an application to generalized fractional differential equations

This article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these co...

Authors: Aftab Hussain, Fahd Jarad and Erdal Karapinar

Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay

This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fraction...

Authors: Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad and Thabet Abdeljawad

Optimal control for obstacle problems involving time-dependent variational inequalities with Liouville–Caputo fractional derivative

We consider an optimal control problem for a time-dependent obstacle variational inequality involving fractional Liouville–Caputo derivative. The obstacle is considered as the control, and the corresponding so...

Authors: Parinya Sa Ngiamsunthorn, Apassara Suechoei and Poom Kumam

Aboodh transform and the stability of second order linear differential equations

In this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stabil...

Authors: Ramdoss Murali, Arumugam Ponmana Selvan, Choonkil Park and Jung Rye Lee

Simplified and improved criteria for oscillation of delay differential equations of fourth order

An interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studyi...

Authors: O. Moaaz, A. Muhib, D. Baleanu, W. Alharbi and E. E. Mahmoud