Article
Engineering, Electrical & Electronic
Ibrahim Ethem Sacu, Mustafa Alci
Summary: This study introduces a new fractional multivibrator topology, which features a multioutput current follower transconductance amplifier (MO-CFTA) and a grounded fractional capacitor for electronically and independently controlling output waveform amplitude, trigger levels, and oscillation period via relevant bias currents. The proposed circuit offers a higher oscillation frequency compared to conventional multivibrators, and has been simulated using SPICE and 0.18 μm TSMC technology, with experimental verification of the introduced concepts.
IETE JOURNAL OF RESEARCH
(2021)
Article
Mathematics, Interdisciplinary Applications
Ivo Petras
Summary: This paper discusses new oscillator structures that include new elements called memory elements, such as memristors, meminductors, and memcapacitors. These circuits can exhibit oscillations and chaotic behavior, and new mathematical models for fractional-order elements and whole oscillator circuits are proposed.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
T. Sathiyaraj, Michal Feckan, JinRong Wang
Summary: This paper investigates the synchronization of fractional order stochastic systems in finite dimensional space, and validates the results through theoretical analysis and numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Multidisciplinary Sciences
Omar Kahouli, Abdellatif Ben Makhlouf, Lassaad Mchiri, Pushpendra Kumar, Naim Ben Ali, Ali Aloui
Summary: This article investigates the existence, uniqueness, and stability of solutions for sigma-Caputo stochastic fractional differential equations using the Banach fixed point technique and stochastic calculus methods. The results are illustrated with three examples.
Article
Mathematics, Interdisciplinary Applications
Jesus M. Munoz-Pacheco, Luis Carlos Lujano-Hernandez, Carlos Muniz-Montero, Akif Akgul, Luis A. Sanchez-Gaspariano, Chun-Biao Li, Mustafa Cagri Kutlu
Summary: This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lu chaotic system based on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The results include simulations in SPICE and experimental measurements confirming the effectiveness and robustness of the system. Compared to passive counterparts, the suggested realizations significantly reduce design and implementation efforts.
Article
Mathematics, Interdisciplinary Applications
Xi Chen, Feng Zheng, Yewen Wei
Summary: This paper explores the role of fractional calculus in circuit systems and compares and studies the effects of three typical calculation methods in different test scenarios using an experimental prototype. It is shown that Oustaloup's rational approximation method usually overestimates the peak-to-peak current and introduces the pulse-voltage phenomenon in piecewise smooth test scenarios, while the results of the two iterative recurrence-form numerical methods are in good agreement with the experimental results. The study aims to provide a reference for efficiently deploying calculation methods in fractional-order piecewise smooth circuit systems, and concludes with some quantitative analysis results.
FRACTAL AND FRACTIONAL
(2023)
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, 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, 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
Engineering, Multidisciplinary
Tamour Zubair, Muhammad Usman, Ilyas Khan, Muqrin A. Almuqrin, Nawaf N. Hamadneh, Abha Singh, Tiao Lu
Summary: In this study, a specific geometry of plasma particles is designed and translated into a mathematical form to study their behavior. Numerical methods are used to validate the model's effectiveness at macroscopic and microscopic scales, highlighting the importance of these tools in plasma research.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Mechanical
Lin He, Chunqiu Wei, Jiang Sha, Delong Mao, Kangshuo Wang
Summary: This paper presents a general numerical scheme for the optimal control problem of fractional Birkhoffian systems. The scheme derives the fractional forced Birkhoff equations and directly discretizes the fractional Pfaff-Birkhoff-d'Alembert principle to convert the original problem into a nonlinear optimization problem. An illustrative example demonstrates the efficiency and simplicity of the proposed method.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Najeeb Alam Khan, Muhammad Ali Qureshi, Saeed Akbar, Asmat Ara
Summary: A new five-dimensional fractional-order chaotic system is proposed based on the Lorenz-Stenflo model with a feedback memristor, which exhibits a two-wing attractor with symmetrical coexistence. The system is found to be unstable and hyperchaotic through stability analysis and Lyapunov exponents calculation. Analogue circuits are implemented for both open-loop and closed-loop memristive systems, and the simulation results show good agreement with numerical simulations. Furthermore, a new cryptographic scheme is presented using random data from the chaotic system for multimedia encryption.
Article
Mathematics, Interdisciplinary Applications
Lu Liu, Jian Wang, Lichuan Zhang, Shuo Zhang
Summary: This paper proposes a multi-AUV dynamic maneuver countermeasure algorithm based on interval information game theory and fractional-order Differential Evolution (DE) to address the challenges posed by the instability of the underwater environment and underwater communication. By establishing advantage function, payoff matrix and Nash equilibrium condition, and utilizing the fractional-order DE algorithm to determine the optimal strategy, the superiority of the algorithm is verified through an example.
FRACTAL AND FRACTIONAL
(2022)
Article
Physics, Multidisciplinary
Vasily E. Tarasov
Summary: Using Luchko's general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is proposed. The nonlocal and general fractional (CF) extensions for probability density functions (PDFs), cumulative distribution functions (CDFs), and probability are defined and their properties are described. Examples of general nonlocal probability distributions of AO are considered. The application of multi-kernel GFC allows for a broader class of operator kernels and nonlocality in probability theory.
Article
Engineering, Electrical & Electronic
Ekrem Cengelci, Muhammet Garip, Ahmed S. Elwakil
Summary: Switching DC/DC converters are closed loop systems that require controllers to stabilize and optimize performance. The K-factor method is a practical way to design these controllers using pole/zero placement adjustment. Extending this method to the fractional-order domain allows for detailed analytical formulas to calculate component values in op-amp-based compensators, with strong correlations between mathematical analysis, circuit simulation, and experimental results.
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS
(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, Hachemi Benaoum, Ahmed S. Elwakil, Mohammad Alshabi
Summary: In this study, the application of fractional-order models in describing impedance and relaxation functions of electrochemical capacitors is reviewed. New q-deformed models based on modified evolution equations are proposed. Experimental verification is conducted using a commercial supercapacitor.
IEEE TRANSACTIONS ON ELECTRON DEVICES
(2022)
Article
Engineering, Biomedical
Abdulwadood Al-Ali, Ahmed Elwakil, Brent Maundy, Sohaib Majzoub
Summary: This study proposes an impedance measurement technique based on wide-band chaotic signals, which enables efficient measurement at low frequencies. The accuracy of the technique was experimentally validated and demonstrated.
BIOMEDICAL MICRODEVICES
(2022)
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
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
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
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.
Article
Engineering, Electrical & Electronic
Amr Elsonbaty, Anis Allagui, Ahmed S. Elwakil
Summary: This work introduces an extended form of the instantaneous spectral analysis technique (E-ISA), which is capable of dealing with nonergodic signal sources with nonstationary spectra and has a smaller bandwidth utilization compared to the standard Fourier transform.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2022)
Article
Computer Science, Information Systems
Sohaib Majzoub, Anis Allagui, Ahmed S. Elwakil
Summary: Impedance spectroscopy is a widely used technique for studying electrochemical and physiological systems. This paper proposes a method and algorithm for computing impedance spectra using time-domain signal excitation. The method offers fast measurement and high accuracy, while avoiding nonlinearity in the samples.
