125 Results Found

This paper presents a new SIRS model for recurrent childhood diseases under the Caputo fractional difference operator. The existence theory is established using Brouwer’s fixed-point theorem and the Banach contraction principle, providing a com...

The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale $\mathcal{Z}$. Moreover, the action of $\mathcal{Q}-$ operator and discrete delta Lapl...

In the present article, we explore the correlation between the sign of a Liouville–Caputo-type difference operator and the monotone behavior of the function upon which the difference operator acts. Finally, an example is also provided to demons...

In this paper, we present a fractional version of the Sakiadis flow described by a nonlinear two-point fractional boundary value problem on a semi-infinite interval, in terms of the Caputo derivative. We derive the fractional Sakiadis model by substi...

This manuscript assesses a semi-analytical method in connection with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). Moreover, we...

In this article, the numerical solution of the mixed Volterra–Fredholm integro-differential equations of multi-fractional order less than or equal to one in the Caputo sense (V-FIFDEs) under the initial conditions is presented with powerful alg...

The questions of the one-value solvability of an inverse boundary value problem for a mixed type integro-differential equation with Caputo operators of different fractional orders and spectral parameters are considered. The mixed type integro-differe...

Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the...

The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maint...

In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown function...

In this paper, the shape of the stability domain $S^q$ for a class of difference systems defined by the Caputo forward difference operator ${\mathsf{\Delta }}^q$ of order $q\in (0,1)$ is numerically analyzed. It is shown numerically that due to of power of the negati...

In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot...

Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractio...

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form ${\Delta }_{\ast }^{\beta }\left[k\right]\left(t\right)=w\left(t+\beta ,k(t+\beta ),k\left(\lambda \right(t+\beta \left)\right)\right)$,...

Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical netwo...

In this study, an integer-order rabies model is converted into the fractional-order epidemic model. To this end, the Caputo fractional-order derivatives are plugged in place of the classical derivatives. The positivity and boundedness of the fraction...

We discuss the solvability of a $(p,q)$-difference equation of fractional order $\alpha \in (1,2]$, equipped with anti-periodic boundary conditions involving the first-order $(p,q)$-difference operator. The desired results are accomplished with the aid o...

This paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like f...

Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and b...

This article deals with analysing the positivity, monotonicity and convexity of the discrete nabla fractional operators with exponential kernels from the sense of Riemann and Caputo operators. These operators are called discrete nabla Caputo–Fa...

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a...

In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We disc...

Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid...

In this study, a time-fractional extension of the classical Theis problem with an exponential source term is investigated in a confined aquifer. The governing equation is modeled using two different fractional derivatives—the Caputo and Atangan...

In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, the multiplicity results of at least three distinct weak solutions are obtained for a new ψ-Caputo-type fractional differe...

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator–prey interaction that follows the fractional-order Rosenzweig–MacAr...

Special functions have been widely used in fractional calculus, particularly for addressing the symmetric behavior of the function. This paper provides improved delta Mittag–Leffler and exponential functions to establish new types of fractional...

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we a...

This paper presents the optimal auxiliary function method (OAFM) implementation to solve a nonlinear fractional system of the Jaulent–Miodek Equation with the Caputo operator. The OAFM is a vital method for solving different kinds of nonlinear...

The chain rule is a foundational concept in calculus, critical for differentiating composite functions, especially those appearing in modern AI techniques. Its extension to fractional calculus presents challenges due to the integral-based nature and...

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis of the said outbreak, mathematical formulations are important techniques that are used for the stability and predictions of infectious disease...

Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly...

In this paper, we study fractional symmetric Hahn difference calculus. The new idea of the symmetric Hahn difference operator, the fractional symmetric Hahn integral, and the fractional symmetric Hahn operators of Riemann–Liouville and Caputo t...

This paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow th...

The fractional reaction–diffusion equation has been used in many real-world applications in fields such as physics, biology, and chemistry. Motivated by the huge application of fractional reaction–diffusion, we propose a numerical scheme...

In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modi...

We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on...

Among the many different definitions of the fractional derivative, the Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider the equations with the Dzhrbashyan–Nersesyan fractional derivative, which gen...

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated wit...

In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary c...

The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In t...

The operational matrices-based computational algorithms are the promising tools to tackle the problems of non-integer derivatives and gained a substantial devotion among the scientific community. Here, an accurate and efficient computational scheme b...

The term convexity associated with the theory of inequality in the sense of fractional analysis has a broad range of different and remarkable applications in the domain of applied sciences. The prime objective of this article is to investigate some n...

This research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schrödinger delay equations (NSDEs) in the context of the Caputo fractional derivative. Using the fr...

Computer networks can be alerted to possible viruses by using kill signals, which reduces the risk of virus spreading. To analyze the effect of kill signal nodes on virus propagation, we use a fractional-order SIRA model using Caputo derivatives. In...

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, we discuss the existence of solutions for a mixed nonlinear differential equation involving a right Caputo fractional derivative operator,...

This paper investigates a car-following model that incorporates both classical and fractional discrete operators. While classical models have been extensively studied, the influence of discrete fractional operators on the stability of such systems ha...

Since polynomial regression models are generally quite reliable for data that can be handled using a linear system, it is important to note that in some cases, they may suffer from overfitting during the training phase. This can lead to negative valu...

The article discusses different schemes for the numerical solution of the fractional Riccati equation with variable coefficients and variable memory, where the fractional derivative is understood in the sense of Gerasimov-Caputo. For a nonlinear frac...

For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time...