Fractal and Fractional, Volume 7, Issue 6

A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, well-known in fluid dynamics, is studied. Namely, the condition $u(x,T)=\beta u(x,0)+\phi \left(x\right)$, where $\beta$ is an arbitrary real number, is proposed in...

This paper aims to establish generalized fractional integral inequalities for operators containing Mittag–Leffler functions. By applying $(\alpha ,h-m)-p$-convexity of real valued functions, generalizations of many well-known inequali...

In this work, an open-source computational–statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport is presented. A parallel implementation of the well-known pseudo-spectral method in addition t...

The symmetric regularized long wave (SRLW) equation is a mathematical model used in many areas of physics; the solution of the SRLW equation can accurately describe the behavior of long waves in shallow water. To approximate the solutions of the equa...

Fractals represent important features of our natural environment, and therefore, several scientific fields have recently begun using fractals that employ fixed-point theory. While many researchers are working on fractals (i.e., Mandelbrot and Julia s...

The skin effect in modeling an induction motor can be described by fractional differential equations. The existing methods for identifying the parameters of an induction motor with a rotor skin effect suggest the presence of errors only in the output...

The control of nonlinear chaotic systems with uncertainties is a challenging problem that has attracted the attention of researchers in recent years. In this paper, we propose a robust adaptive fuzzy fractional control strategy for stabilizing nonlin...

The Cauchy problem for the telegraph equation ${\left(D_t^{\rho }\right)}^{2}u\left(t\right)+2\alpha D_t^{\rho }u\left(t\right)+Au\left(t\right)=f\left(t\right)$ ($0<t\le T,0<\rho <1$, $\alpha >0$), with the Caputo derivative is considered. Here, A is a selfadjoint positive operator, acting in a Hilbert space,...

In this paper, we consider a fully discrete interpolated coefficient mixed finite element method for semilinear time fractional reaction–diffusion equations. The classic $L1$ scheme based on graded meshes and new mixed finite element based on tri...

General fractional calculus (GFC) of operators that is defined through the Mellin convolution instead of Laplace convolution is proposed. This calculus of Mellin convolution operators can be considered as an analogue of the Luchko GFC for the Laplace...

A high-order finite difference numerical scheme based on the compact difference operator is proposed in this paper for time-fractional partial integro-differential equations with a weakly singular kernel, where the time-fractional derivative term is...

In this study, we consider fractional-in-time Venttsel’ problems in fractal domains of the Koch type. Well-posedness and regularity results are given. In view of numerical approximation, we consider the associated approximating pre-fractal prob...

In this article, we investigate the market efficiency of global stock markets using the multifractal detrended fluctuation analysis methodology and analyze the results by dividing them into developed, emerging, and frontier groups. The static analysi...

In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative. The exponential function is replaced by the Mittag–Leffler function, and the kernel depends...

This work introduces a new thermoelastic model of an isotropic and homogeneous annular cylinder. The cylinder’s bounding inner surface is shocked thermally, and the bounding outer surface has no temperature increment and volumetric strain. The...

Dynamical analysis of the incommensurate fractional-order neural network is a novel topic in the field of chaos research. This article investigates a Hopfield neural network (HNN) system in view of incommensurate fractional orders. Using the Adomian...

To provide scientific guidance for the use of foamed concrete (FC) in construction engineering, a thermal conductivity calculation method, based on the fractal model of FC, has been developed. The thermal conductivity (TC) of FC has been tested by th...

In this paper, a four-dimensional competition model, driven by the Riesz–Caputo operator, is established. Then, the presented model’s uniqueness, existence, and stability are discussed. After that, the model is applied to describe the pro...

Fractal geometries consistently provide solutions to several electromagnetic design problems. In this paper, fractal geometries such as Hilbert and Moore curves are used to design efficient High-Impedance Surfaces. Modern communication devices have m...

The block-centered finite-difference method has many advantages, and the time-fractional fourth-order equation is widely used in physics and engineering science. In this paper, we consider variable-coefficient fourth-order parabolic equations of frac...

Interest in studies on fractional calculus and its applications has greatly increased in recent years. Fractional-order analysis has the potential to enhance the dynamic structure of chaotic systems. This study presents the implementation of a lower-...

In this paper, we study a quadratic nonlinear equation from the fractional point of view. An explicit solution is given in terms of the Lambert special function. A new phenomenon appears involving the collapsing of the solution and the blow-up of the...

In real-life control problems, such as power systems, there are large-scale high-ranked discrete-time algebraic Riccati equations (DAREs) from fractional systems that require stabilizing solutions. However, these solutions are no longer numerically l...

A Karman vortex is a phenomenon of fluid flow that can cause fluctuation and vibration. As a result, it leads to fatigue damage to structures and induces safety accidents. Therefore, the analysis of the shedding law and strength of the Karman vortex...

Xylella fastidiosa is a phytobacterium able to provoke severe diseases in many species. When it infects olive trees, it induces the olive quick decline syndrome that leads the tree to a rapid desiccation and then to the death. This phytobacterium has...

As special aggregation functions, overlap functions have been widely used in the soft computing field. In this work, with the aid of overlap functions, two new groups of fuzzy mathematical morphology (FMM) operators were proposed and applied to image...

The unique solvability in the sense of classical solutions for nonlinear inverse problems to differential equations, solved for the oldest Dzhrbashyan–Nersesyan fractional derivative, is studied. The linear part of the equation contains a bound...

This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in...

The aim of this study was to present several improved quantum Hermite–Hadamard-type integral inequalities for convex functions using a parameter. Thus, a new quantum identity is proven to be used as the main tool in the proof of our results. Co...

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics’ fractional Hall effect edge states. The sine-Gordon expansion...

System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex a...

In this paper, we generalize the scheme proposed by Ermakov and Kalitkin and present a class of two-parameter fourth-order optimal methods, which we call Ermakov’s Hyperfamily. It is a substantial improvement of the classical Newton’s met...

Our research focuses on investigating the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations. These equations are defined on an infinite interval and involve non-negative nonlinear terms. Additionally...

The current study presents a comprehensive Lie symmetry analysis for the time-fractional Mikhailov–Novikov–Wang (MNW) system with the Riemann–Liouville fractional derivative. The corresponding simplified equations with the Erd&eacut...

The Rouse formula and its variants have been widely used to describe the vertical distribution of the sediment concentration in sediment-laden flows in equilibrium. Han’s formula extends the Rouse formula to non-equilibrium regimes, where the d...

In the last years of the past century, complex correlation structures were empirically observed, both in aggregated and individual traffic traces, including long-range dependence, large-timescale self-similarity and multi-fractality. The use of stoch...

We consider a system of Riemann–Liouville fractional differential equations with multi-point coupled boundary conditions. Using some techniques from matrix analysis and the properties of the integral operator defined on two Banach spaces, we es...

In this paper, the numerical method for a multiterm time-fractional reaction–diffusion equation with classical Robin boundary conditions is considered. The full discrete scheme is constructed with the L1-finite difference method, which entails...

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discret...

A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive...

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...

In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on...

The paper proposes an adaptive selection method for the shape parameter in the multi-quadratic radial basis function (MQ-RBF) interpolation of two-dimensional (2D) scattered data and achieves good performance in solving integral equations (O-MQRBF)....

Stability analysis over a finite time interval is a well-formulated technique to study the dynamical behaviour of a system. This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the del...

The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematic...

High-quality image restoration is typically challenging due to low signal–to–background ratios (SBRs) and limited statistics frames. To address these challenges, this paper devised a method based on fractional-order total variation (FOTV)...

As a non-homogeneous porous medium, the structural complexity of coal directly affects pore structure parameters and gas percolation characteristics, which in turn determine the fractal dimension of coal samples. Among them, the specific surface area...

In this work, we present a new type of fractional derivatives (FD) involving exponential cotangent function in their kernels called Riemann–Liouville $D^{\sigma ,\gamma }$ and Caputo cotangent fractional derivatives ${}^C{D}^{\sigma ,\gamma }$, respectively,...

The simultaneous estimation of coefficients and the initial conditions for model fractional parabolic systems of porous media is reduced to the minimization of a least-squares cost functional. This inverse problem uses information about the pressures...

This study aims to prove some midpoint-type inequalities for fractional extended Riemann–Liouville integrals. Crucial equality is proven to build new results. Using this equality, several midpoint-type inequalities are established via differentiable...