Relevant bibliographies by topics / First and second fractional derivative test

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Academic literature on the topic 'First and second fractional derivative test'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "First and second fractional derivative test"

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Chii-Huei, Yu. "Study on Some Properties of Fractional Analytic Function." International Journal of Mechanical and Industrial Technology 10, no. 1 (2022): 31–35. https://doi.org/10.5281/zenodo.7016567.

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<strong>Abstract:</strong> In this paper, based on Jumarie&rsquo;s modified Riemann-Liouville (R-L) fractional derivative, we study some properties of fractional analytic function, such as fractional Taylor&rsquo;s theorem, first fractional derivative test, and second fractional derivative test. The major methods used in this paper are fractional Rolle&rsquo;s theorem, fractional mean value theorem, product rule for fractional derivatives, and a new multiplication of fractional analytic functions. In fact, these new results are generalizations of those results in ordinary calculus. <strong>Key
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Fu, Cheng-Biao, Hei-Gang Xiong, and An-Hong Tian. "Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region." Journal of Spectroscopy 2019 (February 3, 2019): 1–11. http://dx.doi.org/10.1155/2019/7159317.

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Discussion on the application of fractional derivative algorithm in monitoring organic matter content in field soil is scarce. This study is aimed at improving the accuracy of soil organic matter (SOM) content estimation in arid region, and the undesirable model precision caused by the missing information associated with the larger discrepancy between conventional integer-order, i.e., first order and second order, derivative, and raw spectral data. We utilized fractional derivative (of zeroth order to second order in 0.2-order interval) processing on the field spectral reflectance (R) of the s
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Syam, Sondos M., Z. Siri, Sami H. Altoum, and R. Md. Kasmani. "Analytical and Numerical Methods for Solving Second-Order Two-Dimensional Symmetric Sequential Fractional Integro-Differential Equations." Symmetry 15, no. 6 (2023): 1263. http://dx.doi.org/10.3390/sym15061263.

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In this paper, we investigate the solution to a class of symmetric non-homogeneous two-dimensional fractional integro-differential equations using both analytical and numerical methods. We first show the differences between the Caputo derivative and the symmetric sequential fractional derivative and how they help facilitate the implementation of numerical and analytical approaches. Then, we propose a numerical approach based on the operational matrix method, which involves deriving operational matrices for the differential and integral terms of the equation and combining them to generate a sin
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Ma, Ruiqun, Min Ni, Quanlong Chen, Yinjia Zhou, and Jinglong Han. "Viscoelastic Fractional Model Based on Harmonic Excitation." Mathematical Problems in Engineering 2022 (July 18, 2022): 1–13. http://dx.doi.org/10.1155/2022/4799387.

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This paper analyzes the viscoelastic fractional constitutive model based on the analytical form of the fractional derivative of the sine (cosine) function. First, the polynomials of the linear model are combined into a fractional derivative term, then the complex modulus can be easily obtained, and the response characteristics of the model can be analyzed. Second, the fractional nonlinear model is expressed in harmonic form, which can easily identify nonlinear parameters. Finally, fractional-order nonlinear models can also be transformed into integer-order nonlinear forms. In this paper, the t
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Molavi-Arabshahi, Mahboubeh, and Zahra Saeidi. "Application of Compact Finite Difference Method for Solving Some Type of Fractional Derivative Equations." International Journal of Circuits, Systems and Signal Processing 15 (September 6, 2021): 1324–35. http://dx.doi.org/10.46300/9106.2021.15.143.

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In this paper, the compact finite difference scheme as unconditionally stable method is applied to some type of fractional derivative equation. We intend to solve with this scheme two kinds of a fractional derivative, first a fractional order system of Granwald-Letnikov type 1 for influenza and second fractional reaction sub diffusion equation. Also, we analyzed the stability of equilibrium points of this system. The convergence of the compact finite difference scheme in norm 2 are proved. Finally, various cases are used to test the numerical method. In comparison to other existing numerical m
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CAFAGNA, DONATO, and GIUSEPPE GRASSI. "FRACTIONAL-ORDER CHUA'S CIRCUIT: TIME-DOMAIN ANALYSIS, BIFURCATION, CHAOTIC BEHAVIOR AND TEST FOR CHAOS." International Journal of Bifurcation and Chaos 18, no. 03 (2008): 615–39. http://dx.doi.org/10.1142/s0218127408020550.

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In this tutorial the chaotic behavior of the fractional-order Chua's circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which enables the solution of the fractional differential equations to be found in closed form. By exploiting the capabilities offered by the decomposition method, the paper presents two remarkable findings. The first result is that a novel bifurcation parameter is identified, that is, the fractional-order q of the derivative. The second result is that chaos exists in the fractional Chua's circuit with
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Bellabaci, Safia, and Bachir Dehda. "Laplacian edge detection method based on a new approximation of the second-order fractional derivative in the Caputo-Fabrizio sense." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e8986. http://dx.doi.org/10.54021/seesv5n2-317.

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Edge detection is an important issue in image processing and computer vision problems. It includes all mathematical methods that aim to identify the discontinuous points in the image. This process leads to construct curves that indicate the boundaries of an object and therefore extract feature information. In recent years, this task has received great attention from researchers and scientists, as we find in the literature many methods with their different algorithms. Up to now, there are two methods, the gradient and Laplacian methods. The first depends on the first derivative, where pixels wi
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Tabak, Abdulsamed. "A novel fractional order PID plus derivative (PIλDµDµ2) controller for AVR system using equilibrium optimizer". COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 40, № 3 (2021): 722–43. http://dx.doi.org/10.1108/compel-02-2021-0044.

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Purpose The purpose of this paper is to improve transient response and dynamic performance of automatic voltage regulator (AVR). Design/methodology/approach This paper proposes a novel fractional order proportional–integral–derivative plus derivative (PIλDµDµ2) controller called FOPIDD for AVR system. The FOPIDD controller has seven optimization parameters and the equilibrium optimizer algorithm is used for tuning of controller parameters. The utilized objective function is widely preferred in AVR systems and consists of transient response characteristics. Findings In this study, results of AV
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Hayat, Afzaal Mubashir, Muhammad Bilal Riaz, Muhammad Abbas, Moataz Alosaimi, Adil Jhangeer, and Tahir Nazir. "Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function." Mathematics 12, no. 13 (2024): 2137. http://dx.doi.org/10.3390/math12132137.

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Fractional differential equations play a significant role in various scientific and engineering disciplines, offering a more sophisticated framework for modeling complex behaviors and phenomena that involve multiple independent variables and non-integer-order derivatives. In the current research, an effective cubic B-spline collocation method is used to obtain the numerical solution of the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. It is implemented with the help of a θ-weighted scheme to solve the proposed problem. The spatial derivative is interpolated using cubic B-spl
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Yee, Jennifer C., and Andrew P. Gould. "An Alternate Method for Minimizing X 2." Publications of the Astronomical Society of the Pacific 137, no. 5 (2025): 054501. https://doi.org/10.1088/1538-3873/adcb6c.

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Abstract In this paper, we describe an algorithm and associated software package (sfit_minimize) for maximizing the likelihood function of a set of parameters by minimizing χ 2. The algorithm estimates the second derivative of the χ 2 function using first derivatives of the function to be fitted and takes fractional, ϵ ≤ 1, steps at each iteration. The derivatives can also be used to calculate the uncertainties in each parameter. We test this algorithm against several standard minimization algorithms in SciPy.optimize.minimize() by fitting point lens models to light curves from the 2018 Korea
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Books on the topic "First and second fractional derivative test"

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Banerjee, Amitava, and Kaleab Asrress. Screening for cardiovascular disease. Edited by Patrick Davey and David Sprigings. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199568741.003.0351.

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Screening involves testing asymptomatic individuals who have risk factors, or individuals who are in the early stages of a disease, in order to decide whether further investigation, clinical intervention, or treatment is warranted. Therefore, screening is classically a primary prevention strategy which aims to capture disease early in its course, but it can also involve secondary prevention in individuals with established disease. In the words of Geoffrey Rose, screening is a ‘population’ strategy. Examples of screening programmes are blood pressure monitoring in primary care to screen for hyp
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Book chapters on the topic "First and second fractional derivative test"

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"Mathematics of Titrimetry." In Practical Volumetric Analysis. The Royal Society of Chemistry, 2014. http://dx.doi.org/10.1039/bk9781849739146-00248.

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In this chapter we focus in more detail on the underpinning quantitative theory of volumetric analysis, starting with solving complex equilibrium problems using the so-called systematic approach to equilibrium. The fractional composition concept is then introduced as a means of representing complex data in a single format. The use of first and second derivative curves and the linearisation of titration data using Gran and Schwartz plots are also discussed.
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Jain, Akshat, Dulendra Damahe, Abhiram Patil, Somya Singh, Priti Singh Sachin, and B. Narkhede. "PSIDIUM GUINEENSE: A REVIEW ON ITS PHARMACOLOGICAL POTENTIAL." In Futuristic Trends in Pharmacy & Nursing Volume 3 Book 17. Iterative International Publishers, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bkpn17p1ch3.

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Psidium guineense is a medicinal plant that has been used traditionally for its curative nature concerning different types of diseases. This review article is concerned with the plant's chemical composition and pharmacological potential for its optimal valuation. Seven phytochemical constituents were isolated from different parts of the shrub by using specified solvents. NMR identified the first chemical constituent as steroid sitosterol. The second compound was identified as triterpene ursolic acid using 1D and 2D NMR. The third compound was recorded as an antioxidant and cytotoxic activity-p
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Sabrina, Yessaadi, and Laskri Mohamed Tayeb. "Edge Detection on Light Field Images." In Research Anthology on Improving Medical Imaging Techniques for Analysis and Intervention. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-7544-7.ch014.

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Digital fundus imaging is becoming an important task in computer-aided diagnosis and has gained an important position in the digital medical imaging domain. One of its applications is the retinal blood vessels extracting. Object detection in machine vision and image processing has gained increasing interest due to its social and security potential. Plenoptic imaging is a promising optical technique. This technique computes the location and the propagation direction information of the object light, which are used as efficient descriptors to detect and track the object displacement. In this chap
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Sabrina, Yessaadi, and Laskri Mohamed Tayeb. "Edge Detection on Light Field Images." In Advances in Healthcare Information Systems and Administration. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7071-4.ch007.

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Digital fundus imaging is becoming an important task in computer-aided diagnosis and has gained an important position in the digital medical imaging domain. One of its applications is the retinal blood vessels extracting. Object detection in machine vision and image processing has gained increasing interest due to its social and security potential. Plenoptic imaging is a promising optical technique. This technique computes the location and the propagation direction information of the object light, which are used as efficient descriptors to detect and track the object displacement. In this chap
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Conference papers on the topic "First and second fractional derivative test"

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Mishra, Asha S. "Application of Fractional Calculus in Reservoir Characterization From Pressure Transient Data in Fractal Reservoir With Phase Redistribution." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86204.

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The present paper describes the use of pressure derivative and second derivative of integral of pressure in a fractal reservoir with matrix participation with phase redistribution in a geological environment that are not possible by conventional techniques. The analysis of this type of data in reservoir characterization is known as “inverse problem” and one can obtain information about interwell and vertical permeability distribution in a reservoir. The fractal geometry in a dynamic pressure transient tests data plays a very vital role for heterogeneity characterization. The pressure transient
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Lorenzo, Carl F., and Tom T. Hartley. "On Self-Consistent Operators With Application to Operators of Fractional Order." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86730.

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This paper extends the idea of the initialization function to the more general concept of a continuation function. The paper sets forth definitions for operator self-consistency which are then applied to test three operators, the ordinary Riemann integral, the time-varying initialized Riemann-Liouville fractional integral, and finally the Caputo derivative. Self-consistency was found for the first two cases. The Caputo fractional derivative operator was found to be self-inconsistent based on possible continuation functions derived from the Laplace transform of the derivative. A theoretical con
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Takeuchi, Yuki, and Reiji Suda. "Second Order Accuracy Finite Difference Methods for Fractional Diffusion Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12059.

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Finite difference methods for fractional differential equation are ever proposed. However, precise error orders have not been analyzed for the methods higher than first order accuracy. This paper proposes a few finite difference methods for fractional diffusion equations and shows our methods have second order accuracy under the conditions that the solution functions have higher order than second order at boundaries. In addition, we show that the accuracy may decrease in the case that the solution functions have lower order than second order at boundaries when we use second order accuracy sche
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Mendlovic, David, Haldun M. Ozaktas, and Adolf W. Lohmann. "Fourier Transforms of Fractional Order and their Optical Interpretation." In Optical Computing. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/optcomp.1993.owd.6.

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The ath power of x, denoted by x a , might be defined as “the number obtained by multiplying unity a times with x”. Thus (2.5)3 = 2.5 x 2.5 x 2.5. This definition makes sense only when a is an integer. However, it is an elementary fact that the definition of the power of a number can be meaningfully and consistently extended to real anil even complex values of a. Likewise, the original definition of the derivative of a function makes sense only for integral orders, i.e. we can speak of the first or second derivative and so on. However, it is possible to extend the definition of the derivative
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Iannitto, Marco, Thomas J. Royston, and Richard L. Magin. "Identifying Fractional Viscoelastic Models Based on Surface Wave Motion." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47769.

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In previous studies of the second author mechanical wave motion on a viscoelastic material representative of biological tissue was analyzed. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and subsurface sources were considered. It was shown that a fractional order Voigt model, in which the damping component, dependent on the first derivative of time, is replaced with a fractional element dependent on a derivative of time of fractional order between 0 and 1, resulted in closer agreement with experiment as compared with the conventional (integer
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Liu, Guoqing, Jie Wang, and Christine Ehlig-Economides. "Modeling of Before Closure Zero Slope Pressure Derivative in a Diagnostic Fracture Injection Test DFIT." In SPE International Hydraulic Fracturing Technology Conference & Exhibition. SPE, 2022. http://dx.doi.org/10.2118/205317-ms.

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Abstract Recent diagnostic fracture injection test (DFIT) data presented on a Bourdet log-log diagnostic plot showed derivative slope of 0 in the before closure (BC) portion of the DFIT response. Some works qualitatively describe it as radial flow. This behavior has not been quantitatively analyzed, modeled and matched. The present work disagrees with the hypothesis of radial flow and successfully matches the relatively flat trend in the Bourdet derivative with a model dominated by friction dissipation coupled with tip extension. The flat trend in Bourdet derivative occurs shortly after shut-i
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Rahman, N. M. Anisur, Hasan A. Nooruddin, and Sukru Sarac. "Improved Identification of Reservoir Heterogeneity with Advanced Derivative Profiles in Relation to Radii of Investigation." In SPE Annual Technical Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/210265-ms.

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Abstract The identification of reservoir heterogeneity is normally attempted by constructing profiles of conventional well-test derivatives with transient-pressure data. Second-order derivatives are more sensitive than the first-order derivatives in the respective profiles with heterogeneity. Under actual operating conditions, the identification of heterogeneity is more complex than under ideal conditions because of the presence of noise. This study investigates how the degree of heterogeneity and the level of noise in the data strike a balance in identifying heterogeneity. In this study, diff
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Aschenbruck, E., R. Blessing, and L. Turanskyj. "FT8-55 Mechanical Drive Aeroderivative Gas Turbine: Design of Power Turbine and Full-Load Test Results." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-343.

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A new, highly efficient 25-MW aero-derivative gas turbine, model FT8-55, has been developed for mechanical drive applications as a member of the FT8 gas turbine family which also includes two generator drive gas turbines, models FT8-30 and FT8-36, with power turbine speeds of 3000 rpm and 3600 rpm, respectively. For the new mechanical drive version FT8-55, the power turbine can be operated up to 5775 rpm at maximum continuous speed. All power turbines are equipped with gas generators, model GG8-1, which are derived from the most popular aero-engine in civil aviation, the JT8D. The first part o
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May, Carl, Henry Wilson, J. Donn Hethcock, and Tim Davis. "Improved Structural Joint Concepts." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81422.

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The joining of composite materials used in airframe structures has always presented a challenge to the structural engineer. As part of a Survivable Affordable Repairable Airframe Program (SARAP) agreement, research on three advanced joining concepts was conducted to identify and validate designs that would provide improved structural efficiency when compared to conventional joining methods. The first involves using finger joints in thin laminates to produce a joint with high specific strength compared to typical joining methods. The second utilizes a derivative of needling for stabilized dry f
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Sesmat, Sylvie, Saïd Chabane, Eric Bideaux, Hubert Lejeune, and Yoann Jus. "Experimental Identification of the Full Opening Time of Pneumatic Valves." In ASME/BATH 2023 Symposium on Fluid Power and Motion Control. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/fpmc2023-110491.

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Abstract Precise determination of the full opening time of ON-OFF pneumatic valves is mandatory especially when they are used as safety elements. This paper proposes a new identification method based on the time at which the tank pressure time derivative is maximum during a charge test. Assuming that the flow is still choked in the valve at least up to this time, it can be shown that this maximum coincides with the full opening. In order to fulfill this condition, a minimal volume for the tank is required according to the valve dynamics and its flow characteristics. Two other conditions have t
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