Article
Engineering, Mechanical
D. Vignesh, Santo Banerjee
Summary: This article investigates the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. The analysis shows that the behavior of the system changes with different fractional orders, highlighting the importance of employing incommensurate order models in real-life modeling.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Electrical & Electronic
Xuejiao Zhao, Shipeng Wang, Qiong Wu, Yanju Ji
Summary: The theory of magnetic-source electromagnetic anomalous diffusion is developed, presenting a multiscale electromagnetic anomalous diffusion theory with improved generalized electrical conductivity. This theory is applied to propose a 3-D modeling method for complex electromagnetic propagation in rough geologic medium, demonstrating improved efficiency and accuracy in detection.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Article
Chemistry, Physical
Weiheng Li, Qiu-An Huang, Yuxuan Bai, Jia Wang, Linlin Wang, Yuyu Liu, Yufeng Zhao, Xifei Li, Jiujun Zhang
Summary: In order to increase the reliability of time-frequency analysis, it is essential to establish a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis. This study formulates a thorough model reduction of fractional impedance spectra for electrochemical energy devices, including the reduction from fractional-order models to integer-order models and from high- to low-order RC circuits, as well as the evolution of characteristic time constants. The results of time-frequency analysis are found to be useful for determining the reduction order and have been validated for various electrochemical energy devices.
Article
Mathematics, Applied
Antonio M. Lopes, J. A. Tenreiro Machado
Summary: This paper explores the performance evaluation and visualization of generalized mean discrete-time fractional controllers using multidimensional scaling, comparing time and frequency responses of controlled systems with different parameter combinations. Numerical experiments with fractional PID and two linear plants demonstrate the feasibility of this method for comparing and visualizing multiple test cases.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Engineering, Electrical & Electronic
Evan Benoit, Joel B. Harley, Cynthia M. Furse
Summary: We evaluate the feasibility of spectral time domain reflectometry (STDR) and spread spectrum time domain reflectometry (SSTDR) as a new modality for impedance measurement. The study focuses on testing energized/noisy systems over a broad frequency spectrum and multiple channels in parallel. Signal parameters of S/SSTDR and their effects on accuracy and usable frequency band are simulated, along with an initial measurement validation. The conclusion includes a recommendation for a viable multichannel impedance measurement system for energized or nonenergized systems in noisy environments.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Mathematics, Interdisciplinary Applications
Ting-Ting Song, Guo-Cheng Wu, Jia-Li Wei
Summary: This study introduces a Hadamard fractional sum based on the time-scale theory and defines h-fractional difference. It proves fundamental theorems and presents initial value problems of fractional difference equations, providing their equivalent fractional sum equations. It also derives the discrete Mittag-Leffler function solutions for linear fractional difference equations. The study concludes that the new discrete fractional calculus of Hadamard type is well defined.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics
Masahiro Yamamoto
Summary: In this study, a framework based on operator theory in fractional Sobolev spaces is constructed to deal with fractional derivatives and time-fractional differential equations. This framework provides a feasible extension of the classical Caputo and the Riemann-Liouville derivatives within Sobolev spaces of fractional orders, including negative ones. It allows for a unified treatment of fractional calculus and time-fractional differential equations.
Article
Mathematics, Applied
Ashraf M. Tawfik, Hamdi M. Abdelhamid
Summary: This paper presents an exact solution for a wide range of fractional diffusion equations with arbitrary time-dependent diffusion coefficients using the Laplace-Fourier technique. The results are validated by examining three common cases of varying diffusivity with time and show exact matching with probability distribution functions and mean square displacements as illustrated in existing literature.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
Summary: This study introduces analytical formulations and finite element solutions for a fractional-order nonlocal plate under both Mindlin and Kirchhoff formulations. By using consistent definitions for fractional-order kinematic relationships, governing equations and boundary conditions are derived based on variational principles. The fractional-order nonlocal model results in a self-adjoint and positive definite system that accepts a unique solution, with a 2D finite element model presented for solving the governing equations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Computer Science, Information Systems
Ioan Burda
Summary: The paper presents theoretical, simulation, and experimental results on the QCM sensor based on the Butterworth van Dyke (BVD) model with lumped reactive motional circuit elements of fractional order. The fractional order BVD model equation of the QCM sensor is derived based on Caputo definitions and its behavior is simulated around the resonant frequencies. The simulations confirm the ability of fractional order calculus to cover a wide range of behaviors beyond experimental practice.
Article
Mathematics, Interdisciplinary Applications
Arran Fernandez, Hafiz Muhammad Fahad
Summary: We conducted a formal study on weighted fractional calculus and its extension, comparing it with classical Riemann-Liouville fractional calculus, proving fundamental properties and solving ordinary differential equations in specific cases.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Vasily E. Tarasov
Summary: This paper proposes a generalization of fractional vector calculus to account for a general form of non-locality, using the general fractional calculus in the Luchko approach. It introduces self-consistent definitions of general fractional differential and integral vector operators.
Article
Mathematics, Interdisciplinary Applications
Abdellatif Ben Makhlouf, Dumitru Baleanu
Summary: This work presents a new approach to study the finite time stability of neutral fractional order systems with time delay, by applying fixed point theory.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Kinda Abuasbeh, Nazim I. Mahmudov, Muath Awadalla
Summary: In this paper, we introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to find a closed form solution for the initial value problem (IVP) of a second-order time-delayed linear system with noncommutative matrices A and omega. We also introduce a delay Gramian matrix and study a relative controllability linear/semi-linear time delay system. We derive the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system and provide sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam-Hyers stability of a second-order semi-linear time-delayed system.
Article
Mathematics, Interdisciplinary Applications
M. A. Gonzalez-Olvera, L. Torres, J. Hernandez-Fontes, E. Mendoza
Summary: The article introduces the use of the Time Fractional Diffusion Equation (TFDE) to model Shipping Water (SW) events. Research found that TFDE has good applicability in describing SW events and shows good consistency with data sets of water free surface elevation.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Electrical & Electronic
Ahmed S. Elwakil, Stavroula Kapoulea, Costas Psychalinos, Anis Allagui
Summary: The study generalizes the Warburg impedance element to a two-port impedance network using an infinite binary tree structure. The Warburg impedance matrix obtained is symmetrical and reciprocal, with an equivalent circuit behavior containing two resistors and a Cole-Davidson type impedance proportional to root 1 + 2/(tau s). Simulation results and implementation in a resonance circuit are provided and discussed.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Ahmed Elwakil, Costas Psychalinos, Brent Maundy, Anis Allagui
Summary: This study explores the possibility of synthesizing capacitive impedances with complex orders and explains the significance of such impedances. The applications of a complex order integrator and a complex order high-pass filter are demonstrated using circuit simulation results.
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS
(2023)
Article
Engineering, Electrical & Electronic
Anis Allagui, Ahmed S. Elwakil, Chunlei Wang
Summary: This paper aims to demonstrate the four possible mapping functions for voltage or charge inputs and their corresponding time-domain or frequency-domain electrical charge outputs when a capacitive device is voltage-charged. Similarly, there are four more possible combinations when the device is current-charged. The dual relationship between each pair of functions is established using single or double Fourier transforms. All eight system functions align only if a constant time- and frequency-independent capacitance is assumed.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Engineering, Electrical & Electronic
Mitar Simic, Todd J. Freeborn, Mladen Veletic, Fernando Seoane, Goran M. Stojanovic
Summary: This article presents a low-complexity method for parameter estimation of the Cole-impedance model suitable for low-cost embedded hardware. The proposed method uses only the measured real and imaginary impedance, without any specific software package/toolbox, or initial values provided by the user. The method has been validated and compared with other relevant work and commercial software, confirming its reliability for bioimpedance processing on embedded hardware.
IEEE SENSORS JOURNAL
(2023)
Article
Electrochemistry
Abdulwadood Al-Ali, Ahmed S. Elwakil, Brent Maundy, Sohaib Majzoub, Anis Allagui
Summary: Electrochemical Impedance Spectroscopy (EIS) is an important diagnostic and monitoring tool in various industries. However, using the conventional frequency-sweep method for EIS in low and ultra low sub-Hz frequencies results in long measurement time. To overcome this issue, a wide-band signal covering the entire frequency range of interest is proposed and validated in this study using the Rudin-Shapiro polynomial. The signal was applied to an RC circuit and compared with the classical frequency-sweep method for verification, and then used for measuring strawberry bio-impedance for age monitoring applications.
JOURNAL OF THE ELECTROCHEMICAL SOCIETY
(2023)
Article
Chemistry, Analytical
Todd J. Freeborn, Shelby Critcher, Gwendolyn Hooper
Summary: This study evaluates the symmetry of fluid shifts in the human body under microgravity. The findings indicate that the fluid shifts induced by a 6-degree body tilt position result in similar changes in both left and right body segments. This has implications for the design of future wearable systems to monitor microgravity-induced fluid shifts.
Article
Electrochemistry
Anis Allagui, Ahmed S. Elwakil
Summary: The capacitance of capacitive energy storage devices cannot be directly measured, but can be estimated from the input and output signals expressed in the time or frequency domains. In this study, Tikhonov's regularization method is used to solve this problem by adding damping to each SVD component, effectively filtering out components corresponding to small singular values and obtaining a stable solution.
ELECTROCHIMICA ACTA
(2023)
Article
Engineering, Electrical & Electronic
Anis Allagui, Di Zhang, Ahmed Elwakil
Summary: This study provides experimental evidence supporting Westerlund's conjecture that Dead Matter Has Memory (Westerlund, 1991). Recent studies have observed and reported memory effects in the dynamic response of electric double-layer capacitors (EDLCs), which integrate their prior history of stimulation and state. Different excitation signals were used to quantify these effects, aiming to charge the same device to the same voltage and accumulated charge level but in different ways. It was observed that different yet repeatable discharge patterns occur, proving the existence of memory. This brief aims to provide further experimental evidence of the inherent memory effect in EDLCs in response to time-varying stationary input excitations with different statistical properties.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Engineering, Electrical & Electronic
Ahmed S. Elwakil, Anis Allagui, Costas Psychalinos, Brent J. Maundy
Summary: We propose a new class of nonlinear resonance networks modeled by second-order nonlinear differential equations. By modifying traditional RLC resonance networks and introducing a variable resistor controlled by one of the circuit's state-space variables, we achieve an embedded self-feedback control mechanism. An experimental verification of the modified series resonance circuit's filter response behavior is also presented.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Chemistry, Analytical
Anis Allagui, Mohammed E. Fouda, Ahmed S. Elwakil, Costas Psychalinos
Summary: This study demonstrates a method to accurately estimate the time-domain power and energy of supercapacitors in response to excitation signals, using only the frequency-domain impedance parameters of the device. The results from simulations and experiments show the feasibility and potential of the proposed procedure.
JOURNAL OF ELECTROANALYTICAL CHEMISTRY
(2023)
Article
Computer Science, Information Systems
Alexandros Pagidas, Costas Psychalinos, Ahmed S. Elwakil
Summary: The frequency behavior of fractional-order, power-law, and double-order filters can be approximated by the same rational integer-order transfer function through curve fitting. Additionally, their implementation can be achieved by the same core with changes in time constants and scaling factors. These findings are experimentally verified using a Field Programmable Analog Array device.
Article
Multidisciplinary Sciences
Mitar Simic, Todd J. Freeborn, Tomislav B. Sekara, Adrian K. Stavrakis, Varun Jeoti, Goran M. Stojanovic
Summary: A novel method for embedded hardware-based parameter estimation of the Cole model of bioimpedance is proposed in this study. The method utilizes a set of derived equations based on measured values of bioimpedance and the numerical approximation of the first derivative of quotient R/X with respect to angular frequency. The accuracy of the proposed method is comparable to existing literature, and performance evaluation is conducted on different embedded-hardware platforms. The results show that Raspberry Pi Pico performs the fastest and with the least energy consumption.
SCIENTIFIC REPORTS
(2023)
Article
Engineering, Biomedical
Shelby Critcher, Patricia Parmelee, Todd J. Freeborn
Summary: The increase in the aging population has led to a higher prevalence of osteoarthritis in the US. Monitoring symptoms of osteoarthritis in a free-living environment can improve understanding of the disease and personalize treatments. This study collected knee tissue bioimpedance and self-reported knee pain data to evaluate their association in older adults with and without knee osteoarthritis.
IEEE OPEN JOURNAL OF ENGINEERING IN MEDICINE AND BIOLOGY
(2023)
Article
Computer Science, Information Systems
Julia Nako, Costas Psychalinos, Ahmed S. Elwakil, Shahram Minaei
Summary: Non-integer order filters can be derived from a generalized structure presented in this work, including fractional-order and power-law filters. These filters can be implemented using a Current Feedback Operational Amplifier as the active element, and can be synthesized using Foster or Cauer RC networks.
Article
Computer Science, Information Systems
Julia Nako, Costas Psychalinos, Ahmed S. Elwakil, Drazen Jurisic
Summary: In this work, higher-order fractional filters with fully controllable frequency characteristics are realized by fitting the filter's magnitude response using a minimum-phase state-space model. Rational integer-order transfer functions are then derived and implemented using Operational Transconductance Amplifiers (OTAs) and a Field Programmable Analog Array (FPAA) device as active elements. The implemented filters can be easily validated on the digitally programmable FPAA platform and have electronic adjustability of their type, order, and characteristic frequencies.
