scholarly journals Impact of fractional order over time response for DC-DC converters with fractional capacitors

2020 ◽  
Vol 25 (2) ◽  
pp. 234-239
Author(s):  
Jesús María López Lezama ◽  
David Esteban Betancur Herrera ◽  
Juan Bernardo Cano ◽  
Nicolás Muñoz Galeano
Keyword(s):  
Steady State ◽  
Fractional Order ◽  
Output Voltage ◽  
Fractional Model ◽  
Switching Model ◽  
Capacitor Voltage ◽  
Fractional Differential ◽  
The Impact ◽  
Fractional Orders ◽  
3D Representations

This paper analyses the impact of fractional orders of derivatives over the response of DC-DC converters which includes fractional capacitors and their parasitic losses for a more realistic approximation of the converter. A fractional model is proposed and is applied for a Boost DC-DC with a fractional capacitor in its DC bus. The fractional model is obtained using Kirchhoff laws and applying the conventional switching model. Then, the resulting set of fractional differential equations is in the Caputo’s sense and was solved using Wavelets method. Solutions were appropriately shown using 3D representations, varying the duty cycle and the fractional order to determine the behaviour of the fractional capacitor voltage, inductor current and output voltage. Ripples and steady state values were determined. Results show high dependence of the fractional order in the variables related to the voltage in the fractional capacitor. With respect to the current, results show that the fractional order does not significantly affect its steady state and ripple.

scholarly journals A Fractional-Order Sequential Hybrid System with an Application to a Biological System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hasib Khan ◽  
Hashim M. Alshehri ◽  
Zareen A. Khan
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Numerical Scheme ◽  
Real Life ◽  
Numerical Approach ◽  
Existence Results ◽  
Alternative Theorem ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Fractional Orders

With the help of Banach’s fixed-point approach and the Leray–Schauder alternative theorem, we produced existence results for a general class of fractional differential equations in this paper. The proposed problem is more comprehensive and applicable to real-life situations. As an example of how our problem might be used, we have created a fractional-order COVID-19 model whose solution is guaranteed by our results. We employed a numerical approach to solve the COVID-19 model, and the results were compared for different fractional orders. Our numerical results for fractional orders follow the same pattern as the classical example of order 1, indicating that our numerical scheme is accurate.

Enhanced frequency shift carrier modulation for H-bridge multilevel converter to conquer the impact of instability in deputize condenser voltage

2018 ◽  
Vol 57 (2) ◽  
pp. 164-174
Author(s):  
Yuvaraja T ◽  
KA Ramesh Kumar
Keyword(s):  
Frequency Shift ◽  
High Power ◽  
Output Voltage ◽  
Harmonic Distortion ◽  
Total Harmonic Distortion ◽  
Multilevel Converter ◽  
Control Scheme ◽  
Capacitor Voltage ◽  
Nonlinear Compensation ◽  
The Impact

H-bridge multilevel converter is the most challenging topology from nominal to high power applications. However, when the energy is exchanged between AC side and DC side or vice versa, the fluctuation in the capacitor used in deputize unit is unavoidable. The fluctuation in the deputize unit is due to the increase in the total harmonic distortion by the capacitor in the output voltages. This total harmonic distortion is evaded by exploring the deputize unit capacitor voltage mathematically. This paper proposes the enhanced frequency shift carrier modulation in H-bridge multilevel converter to suppress the influence of fluctuation in deputize unit capacitor voltages. Enhanced frequency shift carrier modulation is considered for nonlinear compensation. The principal results of using this enhanced frequency shift carrier modulation improvise the total harmonic distortion in the output voltage of H-bridge multilevel converter. Simulation and experimental results are done using MATLAB/SIMULINK to verify the effectiveness of the proposed control scheme.

Global stability and optimal control of a two-patch tuberculosis epidemic model using fractional-order derivatives

2020 ◽  
Vol 13 (03) ◽  
pp. 2050008
Author(s):  
Hossein Kheiri ◽  
Mohsen Jafari
Keyword(s):  
Optimal Control ◽  
Effective Treatment ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Maximum Level ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
Fractional Differential ◽  
The Impact

In this paper, we propose a fractional-order and two-patch model of tuberculosis (TB) epidemic, in which susceptible, slow latent, fast latent and infectious individuals can travel freely between the patches, but not under treatment infected individuals, due to medical reasons. We obtain the basic reproduction number [Formula: see text] for the model and extend the classical LaSalle’s invariance principle for fractional differential equations. We show that if [Formula: see text], the disease-free equilibrium (DFE) is locally and globally asymptotically stable. If [Formula: see text] we obtain sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. We extend the model by inclusion the time-dependent controls (effective treatment controls in both patches and controls of screening on travel of infectious individuals between patches), and formulate a fractional optimal control problem to reduce the spread of the disease. The numerical results show that the use of all controls has the most impact on disease control, and decreases the size of all infected compartments, but increases the size of susceptible compartment in both patches. We, also, investigate the impact of the fractional derivative order [Formula: see text] on the values of the controls ([Formula: see text]). The results show that the maximum levels of effective treatment controls in both patches increase when [Formula: see text] is reduced from 1, while the maximum level of the travel screening control of infectious individuals from patch 2 to patch 1 increases when [Formula: see text] limits to 1.

scholarly journals Integer and Non-Integer Order Study of the GO-W/GO-EG Nanofluids Flow by Means of Marangoni Convection

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 640 ◽  
Author(s):  
Taza Gul ◽  
Haris Anwar ◽  
Muhammad Altaf Khan ◽  
Ilyas Khan ◽  
Poom Kumam
Keyword(s):  
Differential Equation ◽  
Graphene Oxide ◽  
Ethylene Glycol ◽  
Fractional Order ◽  
Marangoni Convection ◽  
Traditional Approach ◽  
Stable Dispersion ◽  
Fractional Differential ◽  
Predictor Corrector ◽  
The Impact

Characteristically, most fluids are not linear in their natural deeds and therefore fractional order models are very appropriate to handle these kinds of marvels. In this article, we studied the base solvents of water and ethylene glycol for the stable dispersion of graphene oxide to prepare graphene oxide-water (GO-W) and graphene oxide-ethylene glycol (GO-EG) nanofluids. The stable dispersion of the graphene oxide in the water and ethylene glycol was taken from the experimental results. The combined efforts of the classical and fractional order models were imposed and compared under the effect of the Marangoni convection. The numerical method for the non-integer derivative that was used in this research is known as a predictor corrector technique of the Adams–Bashforth–Moulton method (Fractional Differential Equation-12) or shortly (FDE-12). The impact of the modeled parameters were analyzed and compared for both GO-W and GO-EG nanofluids. The diverse effects of the parameters were observed through a fractional model rather than the traditional approach. Furthermore, it was observed that GO-EG nanofluids are more efficient due to their high thermal properties compared with GO-W nanofluids.

scholarly journals Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rubayyi T. Alqahtani
Keyword(s):  
Steady State ◽  
Reproduction Number ◽  
Rate Function ◽  
Backward Bifurcation ◽  
Sir Epidemic ◽  
General Incidence Rate ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Steady State Solutions ◽  
Fractional Orders

AbstractIn this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number $R_{0}$ R 0 is less than unity and unstable when $R_{0} > 1$ R 0 > 1 . The analysis shows that the phenomenon of backward bifurcation occurs when $R_{0}<1$ R 0 < 1 . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.

scholarly journals Steady State Behavior of a Single-Switch Non-isolated DC-DC SEPIC Converter Topology with Improved Static Voltage Gain

2021 ◽  
Vol 54 (3) ◽  
pp. 445-452
Author(s):  
D. Murali
Keyword(s):  
Steady State ◽  
Output Voltage ◽  
Voltage Gain ◽  
State Behavior ◽  
Dc Voltage ◽  
Voltage Multiplier ◽  
Capacitor Voltage ◽  
Converter Topology ◽  
Steady State Behavior ◽  
Conversion Technology

This paper presents the analysis of steady state behavior of a single switch non-isolated Single Ended Primary Inductance Converter (SEPIC) topology for achieving high DC voltage gain using diode-capacitor voltage multiplier. A voltage boosting module consisting of inductor and capacitor in addition with two diodes is introduced in the conventional SEPIC configuration in order to derive the DC-DC conversion technology proposed in this work. The voltage gain of the converter is extended using a diode-capacitor voltage multiplier cell. The converter suggested in this work has a single controlled switch. Hence, the conduction losses and the control complexity of the switch are very much reduced. The open loop configuration of the proposed non-isolated converter is described under continuous inductor current mode. The voltage boosting capability of the presented converter is compared with that of the existing modified SEPIC structure. The presented positive output converter topology has low switch voltage-current stress compared to the existing modified SEPIC topology given in the literature. The inductor and capacitor components of the suggested converter are so chosen that the DC output voltage and current waveforms show very low percentage of ripples. A DC voltage level of 24 V is given as input to the proposed converter. The DC voltage obtained across the load terminals is around 370 V which is achievable with low duty ratio (= 0.7) of the active switch. The voltage conversion ratio is very much influenced by the variation of the duty cycle of the power switch. In this work, the converter topology is presented and its various modes of operation are explained with equivalent circuits. The PSIM software platform is effectively and efficiently utilized to validate the performance of the converter. The obtained results convey that the proposed DC-DC conversion technology with extended voltage gain has the capability to maintain the steady-state output voltage and current profiles with almost negligible amount of ripples owing to the use of suitably designed non-dissipative elements in LC filter.

scholarly journals A Fractional Epidemiological Model for Bone Remodeling Process

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abuasbeh
Keyword(s):  
Bone Formation ◽  
Differential Equations ◽  
Fractional Order ◽  
Formation Process ◽  
Differential Model ◽  
Chemical Substances ◽  
Differential Approach ◽  
Fractional Differential ◽  
The Impact ◽  
Calcitonin Secretion

This article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. The first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. The next goal is to investigate how similar is the proposed approach to the method based on system classical differential equations. The dynamical system of equations used is built upon three main parameters. These are chemical substances, namely, calcitonin secretion, osteoclastic and osteoblastic, which are involved in the bone’s formation process. We implement some numerical simulations to graphically show the impact of an arbitrary fractional order of derivative. We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. Flexibility in the choice of the fractional order of derivative is an advantage as it helps in selecting the best fractional order of derivative.

scholarly journals A FRACTAL-FRACTIONAL 2019-NCOV MODEL OF MAJOR DISASTER FOR HUMAN LIFE

Fractals ◽  
2021 ◽  
Author(s):  
SHAHER MOMANI ◽  
R. P. CHAUHAN ◽  
SUNIL KUMAR ◽  
SAMIR HADID
Keyword(s):  
Fractional Order ◽  
Human Life ◽  
Fractal Model ◽  
Practical Situation ◽  
Fractional Model ◽  
Major Disaster ◽  
Spread Dynamics ◽  
Novel Coronavirus ◽  
Fractional Orders

The purpose of this research is to explore the spread dynamics of a novel coronavirus outbreak, or 2019-nCOV via a fractional approach of type fractal-fractional (FF) derivative. We considered the FF approach in sense of the Atangana–Baleanu derivative for the system 2019-nCOV. In the FF operator, when we choose fractional-order one, we achieve the fractal model and when choosing fractal order one then we obtain a fractional model and while considering both the operators together we obtain the fractal-fractional model. The obtained results show via graphics for the different collections of fractal and fractional orders. The graphical results show the new operator impacts on a practical situation in a more visual way.

scholarly journals Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1395
Author(s):  
Charles Castaing ◽  
Christiane Godet-Thobie ◽  
Le Xuan Truong
Keyword(s):  
Fractional Order ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Separable Hilbert Space ◽  
Maximal Monotone ◽  
Fractional Flow ◽  
Order Problem ◽  
Absolutely Continuous ◽  
State Dependent ◽  
Fractional Differential

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

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