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Fractal and Fractional, Volume 7, Issue 1

2023 January - 98 articles

Cover Story: Controlling soft robots is a significant challenge due to the nonlinear elastic nature of the soft materials that conform their structure. This paper studies the identification and control problems of a novel two-degrees-of-freedom, tendon-actuated, soft robotic arm. A decoupled identification approach is presented; later, a fractional order control strategy is proposed and tested experimentally, in comparison with PI solutions. The simulation and experimental results show the goodness of the modeling and control approaches discussed. View this paper
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Articles (98)

  • Article
  • Open Access
4 Citations
2,670 Views
15 Pages

Local Convergence of Traub’s Method and Its Extensions

  • Muhammed Saeed K,
  • Krishnendu Remesh,
  • Santhosh George,
  • Jidesh Padikkal and
  • Ioannis K. Argyros

In this article, we examine the local convergence analysis of an extension of Newton’s method in a Banach space setting. Traub introduced the method (also known as the Arithmetic-Mean Newton’s Method and Weerakoon and Fernando method) wit...

  • Article
  • Open Access
71 Citations
4,076 Views
17 Pages

A major problem in power systems is achieving a match between the load demand and generation demand, where security, dependability, and quality are critical factors that need to be provided to power producers. This paper proposes a proportional&ndash...

  • Article
  • Open Access
3 Citations
2,473 Views
11 Pages

In this paper, we present a class of finite difference methods for numerically solving fractional differential equations. Such numerical schemes are developed based on the change in variable and piecewise interpolations. Error analysis of the numeric...

  • Article
  • Open Access
11 Citations
3,482 Views
26 Pages

Non-Linear Analysis of Novel Equivalent Circuits of Single-Diode Solar Cell Models with Voltage-Dependent Resistance

  • Mahendiran Vellingiri,
  • Muhyaddin Rawa,
  • Sultan Alghamdi,
  • Abdullah A. Alhussainy,
  • Ahmed S. Althobiti,
  • Martin Calasan,
  • Mihailo Micev,
  • Ziad M. Ali and
  • Shady H. E. Abdel Aleem

The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance...

  • Article
  • Open Access
25 Citations
2,279 Views
22 Pages

In this manuscript, we find the numerical solutions of a class of fractional-order differential equations with singularity and strong nonlinearity pertaining to electrohydrodynamic flow in a circular cylindrical conduit. The nonlinearity of the under...

  • Article
  • Open Access
6 Citations
2,552 Views
13 Pages

Power from solar energy is not reliable, due to weather-related factors, which diminishes the power system’s reliability. Therefore, this study suggests a way to predict the intensity of solar irradiance using various statistical algorithms and...

  • Article
  • Open Access
38 Citations
2,904 Views
42 Pages

In this article, we investigate a novel class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. Also, fixed-point techniques are applied to study the existence and uniqueness of a solution to the considered sys...

  • Article
  • Open Access
14 Citations
3,371 Views
18 Pages

Triggered by COVID-19, one of the most dramatic crashes in the stock market in history occurred in March 2020. The sharp reductions in NASDAQ insurance stock indexes were observed after the occurrence of COVID-19 and in March 2020. In this study, the...

  • Article
  • Open Access
1 Citations
2,156 Views
11 Pages

An ε-Approximate Approach for Solving Variable-Order Fractional Differential Equations

  • Yahong Wang,
  • Wenmin Wang,
  • Liangcai Mei,
  • Yingzhen Lin and
  • Hongbo Sun

As a mathematical tool, variable-order (VO) fractional calculus (FC) was developed rapidly in the engineering field due to it better describing the anomalous diffusion problems in engineering; thus, the research of the solutions of VO fractional diff...

  • Article
  • Open Access
69 Citations
4,735 Views
22 Pages

In this article, a fractional-order proportional-integral-differential (FOPID) controller and its modified structure, called a MFOPID controller, are presented. To guarantee optimal system performance, the gains of the proposed FOPID and MFOPID contr...

  • Article
  • Open Access
11 Citations
1,856 Views
26 Pages

This paper gives some results on almost automorphic strong solutions to time-fractional partial differential equations by employing a mix o thef Galerkin method, Fourier series, and Picard iteration. As an application, the existence, uniqueness, and...

  • Article
  • Open Access
8 Citations
2,119 Views
22 Pages

In this paper, existence/uniqueness of solutions and approximate controllability concept for Caputo type stochastic fractional integro-differential equations (SFIDE) in a Hilbert space with a noninstantaneous impulsive effect are studied. In addition...

  • Article
  • Open Access
23 Citations
4,442 Views
18 Pages

A New Look at the Capacitor Theory

  • Manuel Duarte Ortigueira,
  • Valeriy Martynyuk,
  • Volodymyr Kosenkov and
  • Arnaldo Guimarães Batista

The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Sc...

  • Article
  • Open Access
6 Citations
3,528 Views
13 Pages

This research analyzes asymmetric volatility and multifractality in four representative cryptocurrencies using index-based asymmetric multifractal detrended fluctuation analysis. We suggest investigating an idiosyncratic risk premium, which can be ob...

  • Article
  • Open Access
7 Citations
2,874 Views
18 Pages

This study aims to validate the hypothesis that the pharmacokinetics of certain drug regimes are better captured using fractional order differential equations rather than ordinary differential equations. To support this research, two numerical method...

  • Article
  • Open Access
2 Citations
2,784 Views
19 Pages

In this paper, we develop a new class of conservative continuous-stage stochastic Runge–Kutta methods for solving stochastic differential equations with a conserved quantity. The order conditions of the continuous-stage stochastic Runge–K...

  • Article
  • Open Access
74 Citations
3,987 Views
18 Pages

In order to enrich the dynamic behaviors of discrete neuron models and more effectively mimic biological neural networks, this paper proposes a bistable locally active discrete memristor (LADM) model to mimic synapses. We explored the dynamic behavio...

  • Article
  • Open Access
1 Citations
2,282 Views
13 Pages

New Fractional Integral Inequalities Pertaining to Center-Radius (cr)-Ordered Convex Functions

  • Soubhagya Kumar Sahoo,
  • Hleil Alrweili,
  • Savin Treanţă and
  • Zareen A. Khan

In this work, we use the idea of interval-valued convex functions of Center-Radius (cr)-order to give fractional versions of Hermite–Hadamard inequality. The results are supported by some numerical estimations and graphical representations cons...

  • Article
  • Open Access
2,143 Views
12 Pages

In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type o...

  • Article
  • Open Access
3 Citations
2,362 Views
14 Pages

This article investigates the propagation of a deadly human disease, namely leprosy. At the outset, the mathematical model is transformed into a fractional-order model by introducing the Caputo differential operator of arbitrary order. A result is es...

  • Article
  • Open Access
10 Citations
2,477 Views
25 Pages

Metaheuristic Solution for Stability Analysis of Nonlinear Systems Using an Intelligent Algorithm with Potential Applications

  • Faiçal Hamidi,
  • Houssem Jerbi,
  • Hadeel Alharbi,
  • Víctor Leiva,
  • Dumitru Popescu and
  • Wajdi Rajhi

In this article, we provide a metaheuristic-based solution for stability analysis of nonlinear systems. We identify the optimal level set in the state space of these systems by combining two optimization phases. This set is in a definite negative reg...

  • Review
  • Open Access
79 Citations
6,404 Views
29 Pages

A Review on Fractional-Order Modelling and Control of Robotic Manipulators

  • Kishore Bingi,
  • B Rajanarayan Prusty and
  • Abhaya Pal Singh

Robot manipulators are widely used in many fields and play a vital role in the assembly, maintenance, and servicing of future complex in-orbit infrastructures. They are also helpful in areas where it is undesirable for humans to go, for instance, dur...

  • Article
  • Open Access
12 Citations
3,443 Views
29 Pages

Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme

  • Asifa Tassaddiq,
  • Muhammad Tanveer,
  • Muhammad Azhar,
  • Muhammad Arshad and
  • Farha Lakhani

Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques. In this article, we es...

  • Article
  • Open Access
4 Citations
2,392 Views
18 Pages

The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying th...

  • Article
  • Open Access
29 Citations
2,611 Views
22 Pages

The main aim of this paper is to introduce a new class of orthogonal polynomials that generalizes the class of Chebyshev polynomials of the first kind. Some basic properties of the generalized Chebyshev polynomials and their shifted ones are establis...

  • Article
  • Open Access
7 Citations
1,833 Views
20 Pages

Abstract Impulsive Volterra Integro-Differential Inclusions

  • Wei-Shih Du,
  • Marko Kostić and
  • Daniel Velinov

In this work, we provide several applications of (a, k)-regularized C-resolvent families to the abstract impulsive Volterra integro-differential inclusions. The resolvent operator families under our consideration are subgenerated by multivalued linea...

  • Article
  • Open Access
24 Citations
2,218 Views
12 Pages

A new local fractional modified Benjamin–Bona–Mahony equation is proposed within the local fractional derivative in this study for the first time. By defining some elementary functions via the Mittag–Leffler function (MLF) on the Ca...

  • Article
  • Open Access
11 Citations
2,353 Views
23 Pages

New Explicit Propagating Solitary Waves Formation and Sensitive Visualization of the Dynamical System

  • Rana Muhammad Zulqarnain,
  • Wen-Xiu Ma,
  • Sayed M. Eldin,
  • Khush Bukht Mehdi and
  • Waqas Ali Faridi

This work discusses the soliton solutions for the fractional complex Ginzburg–Landau equation in Kerr law media. It is a particularly fascinating model in this context as it is a dissipative variant of the Hamiltonian nonlinear Schrödinger...

  • Article
  • Open Access
9 Citations
4,105 Views
20 Pages

As an essential low-level computer vision task for remotely operated underwater robots and unmanned underwater vehicles to detect and understand the underwater environment, underwater image enhancement is facing challenges of light scattering, absorp...

  • Article
  • Open Access
7 Citations
2,583 Views
14 Pages

LFM Signal Parameter Estimation via FTD-FRFT in Impulse Noise

  • Xuelian Liu,
  • Xuemei Li,
  • Bo Xiao,
  • Chunyang Wang and
  • Bo Ma

LFM signals are widely applied in radar, communication, sonar and many other fields. LFM signals received by these systems contain a lot of noise and outliers. In order to suppress the interference of strong impulse noise on target signals and realiz...

  • Article
  • Open Access
6 Citations
1,905 Views
13 Pages

Aspects related to non-periodicity of a class of complex maps defined in the sense of Caputo like fractional differences and to the asymptotical stability of fixed points are considered. As example the Mandelbrot map of fractional order is considered.

  • Article
  • Open Access
5 Citations
1,962 Views
13 Pages

A fractional wave equation with a fractional Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator A with a discrete spectrum was taken as the elliptic part. We studied the inverse problem of determining the order of th...

  • Article
  • Open Access
31 Citations
2,517 Views
16 Pages

Fractional Dual-Phase-Lag Model for Nonlinear Viscoelastic Soft Tissues

  • Mohamed Abdelsabour Fahmy and
  • Mohammed M. Almehmadi

The primary goal of this paper is to create a new fractional boundary element method (BEM) model for bio-thermomechanical problems in functionally graded anisotropic (FGA) nonlinear viscoelastic soft tissues. The governing equations of bio-thermomech...

  • Article
  • Open Access
2 Citations
1,601 Views
10 Pages

Contrary to the initial-value problem for ordinary differential equations, where the classical theory of establishing the exact unique solvability conditions exists, the situation with the initial-value problem for linear functional differential equa...

  • Article
  • Open Access
13 Citations
3,621 Views
26 Pages

A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise

  • Xiangyu Bai,
  • Dazhi Zhang,
  • Shengzhu Shi,
  • Wenjuan Yao,
  • Zhichang Guo and
  • Jiebao Sun

Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for...

  • Article
  • Open Access
8 Citations
2,468 Views
14 Pages

Scaled Conjugate Gradient for the Numerical Simulations of the Mathematical Model-Based Monkeypox Transmission

  • Suthep Suantai,
  • Zulqurnain Sabir,
  • Muhammad Umar and
  • Watcharaporn Cholamjiak

The current study presents the numerical solutions of a fractional order monkeypox virus model. The fractional order derivatives in the sense of Caputo are applied to achieve more realistic results for the nonlinear model. The dynamics of the monkeyp...

  • Article
  • Open Access
59 Citations
3,715 Views
18 Pages

A New Intelligent Fractional-Order Load Frequency Control for Interconnected Modern Power Systems with Virtual Inertia Control

  • Sherif A. Zaid,
  • Abualkasim Bakeer,
  • Gaber Magdy,
  • Hani Albalawi,
  • Ahmed M. Kassem,
  • Mohmed E. El-Shimy,
  • Hossam AbdelMeguid and
  • Bassel Manqarah

Since modern power systems are susceptible to undesirable frequency oscillations caused by uncertainties in renewable energy sources (RESs) and loads, load frequency control (LFC) has a crucial role to get these systems’ frequency stability bac...

  • Article
  • Open Access
8 Citations
3,148 Views
17 Pages

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

  • Abdellah Bouchendouka,
  • Zine El Abiddine Fellah,
  • Zakaria Larbi,
  • Nicholas O. Ongwen,
  • Erick Ogam,
  • Mohamed Fellah and
  • Claude Depollier

In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the rough...

  • Article
  • Open Access
1 Citations
2,687 Views
28 Pages

Fixed Point for Almost Contractions in v-Generalized b-Metric Spaces

  • Anshuka Kadyan,
  • Savita Rathee,
  • Anil Kumar,
  • Asha Rani and
  • Kenan Tas

We present a significant example to show that the class of v-generalized b-metric spaces properly contains the class of v-generalized metric spaces as well as b-metric spaces. This is accomplished because the example provided by Došenović...

  • Article
  • Open Access
4 Citations
1,879 Views
14 Pages

Topological Structure of Solution Sets of Fractional Control Delay Problem

  • Ahmed A. Al Ghafli,
  • Ramsha Shafqat,
  • Azmat Ullah Khan Niazi,
  • Kinda Abuasbeh and
  • Muath Awadalla

This paper is concerned with the existence of a mild solution for the fractional delay control system. Firstly, we will study the control problem. Then, we will deal with the topological structure of the solution set consisting of the compactness and...

  • Article
  • Open Access
2 Citations
1,722 Views
10 Pages

In this study, we introduce a new definition called δ-contraction. However, we prove some theorems for mappings satisfying the δ-contraction and touch upon fixed points. In the obtained theorems, we also show the existence and uniqueness...

  • Article
  • Open Access
11 Citations
2,699 Views
20 Pages

The Paleocene Kongdian Formation coarse clastic rock reservoir in Bozhong Sag is rich in oil and gas resources and has huge exploration potential. However, the coarse clastic rock reservoir has the characteristics of a complex pore structure and stro...

  • Article
  • Open Access
1 Citations
1,875 Views
16 Pages

In this paper, we consider a time fractional diffusion system with a nonlinear memory term in a bounded domain. We mainly prove some blow-up and global existence results for this problem. Moreover, we also give the decay estimates of the global solut...

  • Article
  • Open Access
7 Citations
2,840 Views
16 Pages

The multifractal relationship between reference evapotranspiration (ET0), computed by the Penmann-Monteith equation (PM), relative humidity (RH) and mean surface temperature (Tmean) was studied in the middle zone of the Guadalquivir River Valley (sou...

  • Article
  • Open Access
11 Citations
4,179 Views
15 Pages

Fractional-Order PID Controller Based on Immune Feedback Mechanism for Time-Delay Systems

  • Adel Makhbouche,
  • Badreddine Boudjehem,
  • Isabela Birs and
  • Cristina I. Muresan

The control of processes with time delays is crucial in process industries such as petrochemical, hydraulic, and manufacturing. It is a challenging task for automation engineers, as it may affect both phase and gain margins. In this case, a robust co...

  • Article
  • Open Access
4 Citations
3,138 Views
25 Pages

Impedance control is widely applied in contact force control for robot manipulators. The traditional impedance model is linear, and has limitations in describing the actual impedance force. In addition, time-varying and dynamic coupling characteristi...

  • Article
  • Open Access
2 Citations
1,579 Views
10 Pages

Exponential Scattering for a Damped Hartree Equation

  • Talal Alharbi,
  • Salah Boulaaras and
  • Tarek Saanouni

This note studies the linearly damped generalized Hartree equation iu˙(Δ)su+iau=±|u|p2(Jγ|u|p)u,0<s<1,a>0,p2. Indeed, one proves an exponential scattering of the energy global solutions, with spherically symmetric datum. This means that...

  • Article
  • Open Access
1 Citations
2,367 Views
38 Pages

A New Method for Controlling Fractional Linear Systems

  • Subramanian V. Shastri,
  • Kumpati S. Narendra and
  • Lihao Zheng

The study of fractional linear time-invariant (LTI) systems has been an area of active research over the past thirty years. Results indicate that such systems are becoming important in the representation of certain types of dynamical behavior in biol...

  • Editorial
  • Open Access
15 Citations
3,493 Views
4 Pages

Fractional-Order System: Control Theory and Applications

  • Thach Ngoc Dinh,
  • Shyam Kamal and
  • Rajesh Kumar Pandey

(Fractional) differential equations have seen increasing use in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry, and many other fields over the last two decades, providing a new and more realistic...

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Fractal Fract. - ISSN 2504-3110