A collection of interdisciplinary applications of fractional-order circuits

Bertsias, Panagiotis; Kapoulea, Stavroula; Psychalinos, Costas; Elwakil, Ahmed S.

doi:10.1016/b978-0-12-824293-3.00007-7

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…It should be noted that the approximation works only when 1/α ∈ Z; otherwise, the approximation itself would involve fractional powers of s [21]. The disadvantage of the Carlson approximation is the large integer order it produces because the number of zeros and poles in Equation (33) increases with k and depends on 1/α. The poles and zeros resulting from the approximation may be complex and are always stable [21].…”

Section: Carlson Approximationmentioning

confidence: 99%

“…The values of the scaling factors k and time constants τ using Equations ( 48) and ( 49) are summarized in Table 9. For the FPAA implementation, the transfer function utilized is in Equation (50), Table 10 shows the substituted coefficients from Equation (48) [33]: The experimental results shown in Figure 15 using the NI ELVIS II show the frequency response within the range of [1, 100k] Hz of the CFE approximation for the low-pass power-law filter of α = 0.5. The difference in the magnitude percentage errors between the ideal response and the approximated curve-fitting FPAA implementation is less than 10%, and it is almost zero at frequencies less than the cut-off frequency, as shown in Figure 15a.…”

Section: Cfe-based Implementation For Low-pass Power-law Filtersmentioning

confidence: 99%

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A Study on Fractional Power-Law Applications and Approximations

Emad,

Hassanein,

AbdelAty

et al. 2024

Electronics

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The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results.

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Section: Carlson Approximationmentioning

confidence: 99%

Section: Cfe-based Implementation For Low-pass Power-law Filtersmentioning

confidence: 99%

A Study on Fractional Power-Law Applications and Approximations

Emad,

Hassanein,

AbdelAty

et al. 2024

Electronics

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“…(17), and then the obtained results are put in Eq. (19). In the final step, we apply D ðkÞδ t on both sides we obtained the following…”

Section: Rpsm Procedures For Fpdes Systemmentioning

confidence: 99%

“…The most powerful tool for researchers to simulate various physical phenomena in applied sciences and nature is known as fractional partial differential equations (FPDEs). The following physical phenomena have been accurately modelled by FPDEs: optics [1], economics [2], fluid traffic [3], electrodynamics [4], hepatitis B virus [5], tuberculosis [6], air foil [7], modelling of earth quack nonlinear oscillation [8], propagation of spherical waves [9], Chaos theory [10], fractional COVID-19 model [11], finance [12], pine wilt disease [13], Zener [14], cancer chemotherapy [15], traffic flow model [16], Poisson-Nernst-Planck diffusion [17], diabetes [18], biomedical and biological [19], and many other numerous applications in various branches of applied mathematics (see [20][21][22]). Due to these numerous applications, FPDEs and factional calculus have gained more attention from researchers as compared to ordinary calculus.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

Khan

Tchier

et al. 2022

Journal of Function Spaces

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In this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed methods are implemented with the Caputo operator. The present techniques are utilised in a very comprehensive and effective manner to obtain the solutions to the suggested fractional-order problems. The nonlinearity of the problem was controlled tactfully. The numerical results of a few examples are calculated and analyzed. The tables and graphs are constructed to understand the higher accuracy and applicability of the current method. The obtained results that are in good contact with the actual dynamics of the given problem, which is verified by the graphs and tables. The present techniques require fewer calculations and are associated with a higher degree of accuracy, and therefore can be extended to solve other high nonlinear fractional problems.

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“…FC is a substitute calculus that may be used to appropriately design a variety of phenomena such as Optics [1], Hepatitis B Virus [3], Tuberculosis [4], Air foil [5], modelling of Earth quack nonlinear oscillation [6], Propagation of Spherical Waves [7], the fluid traffic [8], Chaos theory [9], Finance [11], economics [12], Zener [10], Cancer chemotherapy [13], Electrodynamics [14], heat transfer model [15], the fractional nonlinear space-time nuclear model [16], traffic flow model [17], Poisson-NerstPlanck diffusion [18], Pine wilt disease [19], Diabetes [20], fractional COVID-19 Model [2], biomedical and biological [21] and other applications in various branches of research [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation

Khan

Tchier

et al. 2022

Front. Phys.

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The solutions to fractional differentials equations are very difficult to investigate. In particular, the solutions of fractional partial differential equations are challenging tasks for mathematicians. In the present article, an extension to this idea is presented to obtain the solutions of non-linear fractional Korteweg–de Vries equations. The solutions comparison of the proposed problems is done via two analytical procedures, which are known as the Residual power series method (RPSM) and q-HATM, respectively. The graphical and tabular analysis are presented to show the reliability and competency of the suggested techniques. The comparison has shown the greater contact between exact, RPSM, and q-HATM solutions. The fractional solutions are in good control and provide many important dynamics of the given problems.

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A collection of interdisciplinary applications of fractional-order circuits

Cited by 6 publications

References 25 publications

A Study on Fractional Power-Law Applications and Approximations

A Study on Fractional Power-Law Applications and Approximations

Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation

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