Articles

A fractional derivative with two singular kernels and application to a heat conduction problem

In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present so...

Authors: Dumitru Baleanu, Mohamed Jleli, Sunil Kumar and Bessem Samet

Ulam’s stability for some linear conformable fractional differential equations

In this paper, by introducing the concepts of Ulam type stability for ODEs into the equations involving conformable fractional derivative, we utilize the technique of conformable fractional Laplace transform t...

Authors: Sen Wang, Wei Jiang, Jiale Sheng and Rui Li

On a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary conditions

We investigate the existence of solutions for a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary value conditions. By using Dhage’s fixed point results, we ...

Authors: Dumitru Baleanu, Sina Etemad and Shahram Rezapour

Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law

In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed poi...

Authors: Mohammed S. Abdo, Satish K. Panchal, Kamal Shah and Thabet Abdeljawad

Impact of reduction in contact time activity of infected individuals on the dynamics and control of directly transmitted respiratory infections in SIR models

This paper aims to study the impact of using an educational strategy on reducing the efforts needed to control respiratory transmitted infections represented by SIR models, taking into account heterogeneity in...

Authors: Muntaser Safan

Parameter interval of positive solutions for a system of fractional difference equation

This paper deals with a typical system of Caputo fractional difference equations. Using the Guo–Krasnosel’skii fixed point theorem, we find a parameter interval for which at least one positive solution of the ...

Authors: Kazem Ghanbari and Tahereh Haghi

Fractional operators for the Wright hypergeometric matrix functions

In this paper, we contribute to the results of Bakhet et al. (Integral Transforms Spec. Funct. 30:138–156, 2019) by applying fractional operators to the Wright hypergeometric matrix functions. We give matrix recu...

Authors: M. Abdalla

Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers

The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds. For this purpose, we first introduce Jindalrae–Stirl...

Authors: Taekyun Kim, Dae San Kim, Lee-Chae Jang and Hyunseok Lee

A preconditioned fast collocation method for a linear bond-based peridynamic model

We develop a fast collocation method for a static bond-based peridynamic model. Based on the analysis of the structure of the stiffness matrix, a fast matrix-vector multiplication technique was found, which ca...

Authors: Xuhao Zhang, Xiao Li, Aijie Cheng and Hong Wang

Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations

Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequali...

Authors: Vahid Parvaneh, Maryam Khorshidi, Manuel De La Sen, Hüseyin Işık and Mohammad Mursaleen

Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments

It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equa...

Authors: Zonghong Feng, Yong Wang and Xin Ma

Existence and uniqueness for fuzzy differential equation with Hilfer–Katugampola fractional derivative

In this paper, we study a kind of fuzzy differential equation with Hilfer–Katugampola fractional derivative and nonlocal condition. By using successive approximation method, we obtain some sufficient condition...

Authors: Xingru Chen, Haibo Gu and Xingzhao Wang

Study on the estimates of Gronwall–Ou-Iang dynamic integral inequalities by means of diamond-α derivatives

By the utilization of diamond-α derivatives, certain new generalizations of Ou-Iang type of dynamic integral inequalities of one independent variable on time scales are examined. The resulting inequalities are si...

Authors: Zareen A. Khan

A coupled system of generalized Sturm–Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives

In this paper, we study a coupled system of generalized Sturm–Liouville problems and Langevin fractional differential equations described by Atangana–Baleanu–Caputo (ABC for short) derivatives whose formulatio...

Authors: D. Baleanu, J. Alzabut, J. M. Jonnalagadda, Y. Adjabi and M. M. Matar

Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting

In this paper, we prpose a single-species stage structure model with Michaelis–Menten-type harvesting for mature population. We investigate the existence of all possible equilibria of the system and discuss th...

Authors: Xiangqin Yu, Zhenliang Zhu, Liyun Lai and Fengde Chen

The influence of fear effect to the Lotka–Volterra predator–prey system with predator has other food resource

A Lotka–Volterra predator–prey system incorporating fear effect of the prey and the predator has other food resource is proposed and studied in this paper. It is shown that the trivial equilibrium and the pred...

Authors: Zhenliang Zhu, Runxin Wu, Liyun Lai and Xiangqin Yu

White noise theory and general improved Kudryashov method for stochastic nonlinear evolution equations with conformable derivatives

The aim of this work is to investigate the Wick-type stochastic nonlinear evolution equations with conformable derivatives. The general Kudryashov method is improved by a new auxiliary equation. So, a new tech...

Authors: Abd-Allah Hyder

Alpha fractional frequency Laplace transform through multiseries

Our main goal in this work is to derive the frequency Laplace transforms of the products of two and three functions with tuning factors. We propose the Laplace transform for certain types of multiseries of cir...

Authors: Meganathan Murugesan, Thabet Abdeljawad, Britto Antony Xavier Gnanaprakasam and Fahd Jarad

High-order compact scheme for the two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

In this article, an unconditionally stable compact high-order iterative finite difference scheme is developed on solving the two-dimensional fractional Rayleigh–Stokes equation. A relationship between the Riem...

Authors: Muhammad Asim Khan and Norhashidah Hj. Mohd Ali

Reliable methods to study some nonlinear conformable systems in shallow water

In this paper, consider the eminent coupled Boussinesq–Burger (BB) equations and the coupled Whitham–Broer–Kaup (WBK) equations with time fractional derivative arising in the investigation of shallow water wav...

Authors: Altaf A. Al-Shawba, Farah A. Abdullah, Amirah Azmi and M. Ali Akbar

Existence of nonoscillatory solutions tending to zero of third-order neutral dynamic equations on time scales

We study the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations on time scales by employing Krasnoselskii’s fixed point theorem. Two examples ar...

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

Stabilization of the weakly coupled plate equations with a locally distributed damping

In this paper, we study the indirect stabilization of a system of plate equations which are weakly coupled and locally damped. By virtue of the general results due to Burq in the study of asymptotic behavior o...

Authors: Xianzheng Zhu

Further extension of Voigt function and its properties

In this paper, by using the confluent hypergeometric function of the first kind, we propose a further extension of the Voigt function and obtain its useful properties as (for example) explicit representation a...

Authors: Nabiullah Khan, Mohd Ghayasuddin, Waseem A. Khan, Thabet Abdeljawad and Kottakkaran Sooppy Nisar

Identification of chaos in fractional chaotic map

This paper utilizes the 0–1 test algorithm to identify chaos in a fractional chaotic map. A fractional Burgers map is proposed by means of the Caputo-like delta difference operator. The bifurcation diagrams, p...

Authors: Jie Ran

Solvability of non-semicontinuous systems of Stieltjes differential inclusions and equations

We prove an existence result for systems of differential inclusions driven by multivalued mappings which need not assume closed or convex values everywhere, and need not be semicontinuous everywhere. Moreover,...

Authors: Rodrigo López Pouso, Ignacio Márquez Albés and Jorge Rodríguez-López

Existence of solutions of infinite system of nonlinear sequential fractional differential equations

In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improv...

Authors: Zahra Ahmadi, Rahmatollah Lashkaripour, Hamid Baghani, Shapour Heidarkhani and Giuseppe Caristi

Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative

In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boun...

Authors: Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Kanokwan Sitthithakerngkiet and Alhassan Ibrahim

Existence and uniqueness of periodic solutions for a system of differential equations via operator methods

Authors: Ruixiong Fan and Chengbo Zhai

New insights on weighted pseudo almost periodic solutions in a Lasota–Wazewska system

We study the weighted pseudo almost periodic solutions of a Lasota–Wazewska system. With the aid of fixed point theory and differential inequality strategies, we give a set of new sufficient criteria that guar...

Authors: Changjin Xu, Maoxin Liao, Peiluan Li and Shuai Yuan

Homotopy-Sumudu transforms for solving system of fractional partial differential equations

In this paper, we investigate the Sumudu transforms and homotopy analysis method (S-HAM) for solving a system of fractional partial differential equations. A general framework for solving such a kind of proble...

Authors: A. K. Alomari

Random attractors for non-autonomous stochastic wave equations with nonlinear damping and white noise

This paper is concerned with the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with additive white noise, for which the nonlinear damping has a critical cubic growth rate. By sh...

Authors: Huazhen Yao and Jianwen Zhang

Some new hybrid power mean formulae of trigonometric sums

We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formu...

Authors: Li Chen and Zhuoyu Chen

On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series

In this paper a general framework is presented on some operational properties of Caputo modification of Hadamard-type fractional differential operator along with a new algorithm proposed for approximation of H...

Authors: Rashida Zafar, Mujeeb ur Rehman and Moniba Shams

α-ψ-contractions and solutions of a q-fractional differential inclusion with three-point boundary value conditions via computational results

We review the existence of solutions for a three-point nonlinear q-fractional differential equation and also its related inclusion. In this way, we use α-ψ-contractions and multifunctions. Also, we provide two ex...

Authors: Sina Etemad, Shahram Rezapour and Mohammad Esmael Samei

Integral inequalities for s-convex functions via generalized conformable fractional integral operators

We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and p...

Authors: Artion Kashuri, Sajid Iqbal, Rozana Liko, Wei Gao and Muhammad Samraiz

Chaotic triopoly game: a congestion case

In this paper, we propose a simple network consisting of only two nodes and two paths. The first node, which is called the source, has three competing firms that send their quantities of load via the two paths...

Authors: S. S. Askar and A. Al-khedhairi

Classical stabilities of multiplicative inverse difference and adjoint functional equations

Authors: B. V. Senthil Kumar, Khalifa Al-Shaqsi and Hemen Dutta

Global existence of classical solutions for two-dimensional isentropic compressible Navier–Stokes equations with small initial mass

In this paper, we consider the initial-boundary value problem of two-dimensional isentropic compressible Navier–Stokes equations with vacuum on the square domain. Based on the time-weighted uniform estimates, ...

Authors: Wei Li, Zhaoyang Shang and Fuquan Tang

On the solutions of a max-type system of difference equations of higher order

Authors: Guangwang Su, Caihong Han, Taixiang Sun and Lue Li

Sharing values of q-difference-differential polynomials

This paper is devoted to the uniqueness of q-difference-differential polynomials of different types. Using the idea of common zeros and common poles (Chin. Ann. Math., Ser. A 35:675–684, 2014), we improve the con...

Authors: Jian Li and Kai Liu

Hopf bifurcation control for the main drive delay system of rolling mill

In this work, the Hopf bifurcation of the main drive delay system of rolling mill is controlled and analyzed by designing a nonlinear controller. The time-delay is selected as a bifurcation parameter, and the ...

Authors: Jinbin Wang, Lifeng Ma and Yong Wang

Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel

In this work, we study the problem to identify an unknown source term for the Atangana–Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the...

Authors: Nguyen Huu Can, Nguyen Hoang Luc, Dumitru Baleanu, Yong Zhou and Le Dinh Long

Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation

Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative prope...

Authors: Rabia Ilyas Butt, Thabet Abdeljawad and Mujeeb ur Rehman

Existence and monotone iteration of unique solution for tempered fractional differential equations Riemann–Stieltjes integral boundary value problems

The primary objective of this research paper is to investigate two kinds of high-order tempered fractional differential equations integral boundary value problems. By means of the mixed monotone operators fixe...

Authors: Bibo Zhou, Lingling Zhang, Nan Zhang and Emmanuel Addai

M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water

In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including...

Authors: Onur Alp Ilhan, Jalil Manafian, As’ad Alizadeh and Sizar Abid Mohammed

Study on a susceptible–exposed–infected–recovered model with nonlinear incidence rate

A stochastic susceptible–exposed–infected–recovered (SEIR) model with nonlinear incidence rate is investigated. Under suitable conditions, existence and uniqueness of a global solution, stationary distribution...

Authors: Lijun Chen and Fengying Wei

A new model of economic order quantity associated with a generalized conformable differential-difference operator

The economic order quantity (EOQ) is the order quantity that minimizes the total holding costs and ordering costs. In this effort, we propose a design for EOQ by employing a conformable differential-difference...

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

Global continuum and multiple positive solutions to one-dimensional p-Laplacian boundary value problem

We show the global structure of the set of positive solutions of a discrete Dirichlet problem involving the p-Laplacian difference operator suggesting suitable conditions on the weight function and nonlinearity. ...

Authors: Liping Wei and Ruyun Ma

On Grüss inequalities within generalized K-fractional integrals

Authors: Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Khalida Inayat Noor, Dumitru Baleanu and Jia-Bao Liu

Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics

The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction...

Authors: Nauman Ahmed, Muhammad Rafiq, Dumitru Baleanu, Ali Saleh Alshomrani and Muhammad Aziz-ur Rehman