Fractal and Fractional, Volume 7, Issue 3

Road traffic networks are chaotic and highly complex systems. In this paper, we introduce a dynamic gravity model that characterizes the behaviors of the O-D (origin-destination) traffic, such as equilibrium, period-doubling, chaos, and fractal in di...

Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. In this paper, we present a spectral collocation method with tempered fractional Jacobi functions (TFJFs) as basis functions and obtain an efficient algorithm t...

We analyze an extension of the dual-phase lag model of thermal diffusion theory to accurately predict the contribution of thermoelastic bending (TE) to the Photoacoustic (PA) signal in a transmission configuration. To achieve this, we adopt the parti...

Motivated by the increase in practical applications of fractional calculus, we study the classical gradient method under the perspective of the $\psi$-Hilfer derivative. This allows us to cover several definitions of fractional derivatives that are fo...

This paper proposed a dead-time compensation method with fractional-order proportional integral (FOPI) error voltage control. The disturbance voltages caused by the power devices’ dead time and non-ideal switching characteristics are compensate...

Pore space of tight sandstone samples exhibits fractal characteristics. Nuclear magnetic resonance is an effective method for pore size characterization. This paper focuses on fractal characteristics of pore size from nuclear magnetic resonance (NMR)...

In this work, we demonstrate that it is possible to create supervised machine-learning models using a support vector machine and random forest algorithms to separate yeast cells exposed to hyperosmotic stress from intact cells. We performed fractal,...

We provide streamlined criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. We use a comparison approach with first-order equations that have standard os...

This work examines a new subclass of generalized bi-subordinate functions of complex order $\gamma$ connected to the q-difference operator. We obtain the upper bounds ${\rho }_m$ for generalized bi-subordinate functions of complex order $\gamma$ using the F...

Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional Fourier transform (FRFT), as an extension of the Fourier transform, is particularly important due to the design of its qua...

This paper deals with the problem of group consensus for a fractional-order multi-agent system (FOMAS) without considering the intergroup balance condition. By adopting a dynamic event-triggered mechanism, the updating frequency of control input is s...

Technological innovation, the financial market, and the real economy are mutually promoting and restricting. Considering the interference of market-noise information, this paper applies the wavelet-denoising method of the soft- and hard-threshold com...

Fractional differential operators have recently been linked with numerous other areas of science, technology and engineering studies. For a real variable, the class of fractional differential and integral operators is evaluated. In this study, we loo...

One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-simi...

When an electro-optical tracking system (ETS) needs higher control precision, system identification can be considered to improve the accuracy of the system, so as to improve its control effect. The fractional system model of ETS can describe the char...

The Caputo fractional $\alpha$-derivative, $0<\alpha <1$, for non-smooth functions with $1+\alpha$ regularity is calculated by numerical computation. Let I be an interval and ${\mathcal{D}}_{\alpha }\left(I\right)$ be the set of all functions $f\left(x\right)$ which satisfy $f\left(x\right)=f\left(c\right)+f^{\&pr}$...

The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal...

In this research, three numerical methods, namely the variational iteration method, the Adomian decomposition method, and the homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differe...

In this paper, we study some relations between different weights in the classes ${\mathcal{B}}_p,$${\mathcal{B}}_p^{*},$${\mathcal{M}}_p$ and ${\mathcal{M}}_p^{*}$ that characterize the boundedness of the Hardy operator and the adjoint Hardy operator. We also prove that these classes generate the same weighted Lore...

In this study, we aim to provide reliable methods for the initial value problem of the fractional modified Korteweg–de Vries (mKdV) equations. Fractional differential equations are essential for more precise simulation of numerous processes. Th...

In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate poten...

This study uses fractal analysis to measure the detailed intensity of well-known Classical and Renaissance façades. The study develops a method to understand their interrelated design principles more comprehensively. With this evaluation tool, one ca...

Based on the fact that the inductor and capacitor are of a non-integer order by nature, to provide a more accurate theoretical basis for the optimal control of the converter, the fractional-order model of the Buck-Boost converter in the continuous mo...

In this study, the extended ${\mathrm{G}}^{\prime }/\mathrm{G}$ method is used to investigate the space–time fractional Burger-like equation and the space–time-coupled Boussinesq equation with M-truncated derivative, which have an important place in fluid dynamic...

In this paper, we give an efficient way to calculate the values of the Mittag–Leffler (h-ML) function defined in discrete time $h\mathbb{N}$, where $h>0$ is a real number. We construct a matrix equation that represents an iteration scheme obtained from a...

The study proposes a novel chaotic system with a cubic non-linear term. Different system characteristics are investigated including equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. Also, the electronic circu...

Nonlinear fractional partial differential equations (NLFPDEs) are widely used in simulating a variety of phenomena arisen in several disciplines such as applied mathematics, engineering, physics, and a wide range of other applications. Solitary wave...

In this research, a model is proposed using piecewise fractal theory that considers abrasive and adhesive wear. The model demonstrated improved wear computation accuracy of a contact mechanical seal end face. The validity of the model was established...

In this paper, we analyze the well-posedness of the Cauchy–Dirichlet problem to an integro-differential equation on a multidimensional domain $\Omega \subset {\mathbb{R}}^n$ in the unknown $u=u(x,t)$, ${\mathbf{D}}_t^{{\nu }_0}\left({\varrho }_{0}u\right)-{\mathbf{D}}_t^{{\nu }_1}({\varrho }_{1}u$...

The design of advanced robust control is crucial for serial robotic manipulators under various uncertainties and disturbances in case of the forceful performance needs of industrial robotic applications. Therefore, this work has proposed the design a...

Global stability criteria for Λ-fractional Mechanics are established. The fractional extension of a bar under axial loading is discussed. Globally minimizing the total energy function, non-smooth deformations are introduced. The co-existence o...

In this study, we proposed a sliding mode control method based on fixed-time sliding mode surface for the synchronization of uncertain fractional-order hyperchaotic systems. In addition, we proposed a novel self-evolving non-singleton-interval type-2...

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices for fractional integration, we try to solve those system...

This paper investigates the state prediction problems for uncertain Euler–Lagrange systems with large time delays during data transmissions. A set of sequential predictors is proposed to estimate the actual real-time states of the systems by us...

This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs). We construct explicit and implicit FORK methods for FDEs by using the Caputo...

The model of multiple trapping into energy-distributed states is a successful tool to describe the transport of nonequilibrium charge carriers in amorphous semiconductors. Under certain conditions, the model leads to anomalous diffusion equations tha...

Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-co...

Mean relative entropy has a wide range of applications in measuring information differences. However, relative entropy is difficult to approximate from empirical distribution entropy. Therefore, we replace the probability density function in the mean...

In this paper, we study the nonlinear Riesz space-fractional convection–diffusion equation over a finite domain in two dimensions with a reaction term. The Crank–Nicolson difference method for the temporal and the weighted–shifted G...

A comb structure consists of a one-dimensional backbone with lateral branches. These structures have widespread application in medicine and biology. Such a structure promotes an anomalous diffusion process along the backbone (x-direction), along with...

We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral b...

In the search for causes and cures of cancer diseases, many mathematical models developed have resulted in systems of nonlinear stiff ordinary differential equations. With these models, many numerical estimates of biological knowledge of the paramete...

Proper control is necessary for ensuring that UAVs successfully navigate their surroundings and accomplish their intended tasks. Undoubtedly, a perfect control technique can significantly improve the performance and reliability of UAVs in a wide rang...

In this paper, we study g-fractional diffusion on bounded domains in ${\mathbb{R}}^d$ with absorbing boundary conditions. A new general and explicit representation of the solution is obtained. We study the first-passage time distribution, showing the dependence on...

Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impa...

The development of certain aspects of special polynomials in line with the monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research....

Adaptive control is essential and effective for reliable quadrotor operations in the presence of uncertain modeling parameters and unknown time-delayed inputs. This paper presents an original radial basis function neural network-based adaptive fracti...

The purpose of this survey is twofold. First, we survey the studies of percolation on fractal networks. The objective is to assess the current state of the art on this topic, emphasizing the main findings, ideas and gaps in our understanding. Secondl...

The role of fractional calculus in circuit systems has received increased attention in recent years. In order to evaluate the effectiveness of time-domain calculation methods in the analysis of fractional-order piecewise smooth circuit systems, an ex...

In this article, we study the existence of a solution to the mixed hybrid fractional differential equations of sequential type with nonlocal integral hybrid boundary conditions. The main results are established with the aid of Darbo’s fixed poi...