Relevant bibliographies by topics / Fractional derivative

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fractional derivative'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Fractional derivative"

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TARASOV, VASILY E. "FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE." International Journal of Mathematics 18, no. 03 (2007): 281–99. http://dx.doi.org/10.1142/s0129167x07004102.

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Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
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Feng, Xiaobing, and Mitchell Sutton. "A new theory of fractional differential calculus." Analysis and Applications 19, no. 04 (2021): 715–50. http://dx.doi.org/10.1142/s0219530521500019.

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This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize what functions are fractionally differentiable. Various calculus rules including a fundamental theorem calculus, product and chain rules, and integration by parts formulas are established for weak fractional derivatives. Additionally, relationsh
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Lazopoulos, Anastasios K., and Dimitrios Karaoulanis. "Fractional Derivatives and Projectile Motion." Axioms 10, no. 4 (2021): 297. http://dx.doi.org/10.3390/axioms10040297.

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Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.
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Farayola, Musiliu Folarin, Sharidan Shafie, Fuaada Mohd Siam, Rozi Mahmud, and Suraju Olusegun Ajadi. "Mathematical modeling of cancer treatments with fractional derivatives: An Overview." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (2021): 389–401. http://dx.doi.org/10.11113/mjfas.v17n4.2062.

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This review article presents fractional derivative cancer treatment models to show the importance of fractional derivatives in modeling cancer treatments. Cancer treatment is a significant research area with many mathematical models developed by mathematicians to represent the cancer treatment processes like hyperthermia, immunotherapy, chemotherapy, and radiotherapy. However, many of these models were based on ordinary derivatives and the use of fractional derivatives is still new to many mathematicians. Therefore, it is imperative to review fractional cancer treatment models. The review was
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Chanchlani, Lata, Pratibha Manohar, Ajay Sharma, and Sangeeta Choudhary. "Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives." Indian Journal Of Science And Technology 17, no. 16 (2024): 1702–12. http://dx.doi.org/10.17485/ijst/v17i16.2514.

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Objectives: The aim is to establish prerequisite properties for the Hilfer-Hadamard fractional derivatives and address boundary value problems related to fractional polar Laplace and fractional Sturm-Liouville equations involving Hilfer-Hadamard fractional derivatives. Methods: Existing definitions and findings are utilized to obtain the properties for fractional derivatives, and the Adomian decomposition method is employed to solve the fractional differential equations. Findings: Validity conditions for the law of exponents are determined, and the study investigates the fractional differentia
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Khurshaid*, Adil, and Hajra Khurshaid. "Comparative Analysis and Definitions of Fractional Derivatives." Journal of Biomedical Research & Environmental Sciences 4, no. 12 (2023): 1684–88. http://dx.doi.org/10.37871/jbres1852.

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Fractional Calculus (FC) has emerged as a valuable tool in various fields. This study explores the historical development of (FC) and examines prominent definitions regarding Fractional Derivatives (FD), such as the Riemann-Liouville, Grunwald-Letnikov, Caputo Fractional Derivative, Katugampula derivatives, Caputo Fractional Derivative, Caputo-Fabrizio Fractional Derivative and as well as Atangana-Baleanu Fractional Derivative. It critically evaluates their strengths, weaknesses and implications on (FD) equations. The findings contribute to establishing a clearer understanding of Fractional De
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Hattaf, Khalid. "A New Mixed Fractional Derivative with Applications in Computational Biology." Computation 12, no. 1 (2024): 7. http://dx.doi.org/10.3390/computation12010007.

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This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. This developed definition encompasses many types of fractional derivatives, such as the Riemann–Liouville and Caputo fractional derivatives for singular kernel types, as well as the Caputo–Fabrizio, the Atangana–Baleanu, and the generalized Hattaf fractional derivatives for non-singular kernel types. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, a novel numerical scheme is d
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Kaya, U. "CAUCHY FRACTIONAL DERIVATIVE." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 12, no. 4 (2020): 28–32. http://dx.doi.org/10.14529/mmph200403.

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In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.
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Hattaf, Khalid. "On Some Properties of the New Generalized Fractional Derivative with Non-Singular Kernel." Mathematical Problems in Engineering 2021 (May 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/1580396.

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This paper presents some new formulas and properties of the generalized fractional derivative with non-singular kernel that covers various types of fractional derivatives such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. These new properties extend many recent results existing in the literature. Furthermore, the paper proposes some interesting inequalities that estimate the generalized fractional derivatives of some specific functions. These inequalities can be used to construct Lyapunov funct
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Guswanto, Bambang Hendriya, Leony Rhesmafiski Andini, and Triyani Triyani. "On Conformable, Riemann-Liouville, and Caputo fractional derivatives." Bulletin of Applied Mathematics and Mathematics Education 2, no. 2 (2022): 59–64. http://dx.doi.org/10.12928/bamme.v2i2.7072.

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This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations of the solutions. The result shows that conformable fractional derivative can be used as an alternative to Riemann-Liouville and Caputo fractional derivative for order α with 1/2<α<1.
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Dissertations / Theses on the topic "Fractional derivative"

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Guariglia, Emanuel. "Fractional derivative of the riemann zeta function." Doctoral thesis, Universita degli studi di Salerno, 2017. http://hdl.handle.net/10556/2611.

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2015 - 2016<br>In this work of thesis, the Riemann zeta function was studied by using an unconventional approach. The reason for choosing this approach was to explore the many applications that the Riemann zeta has not only in pure mathematics, but also in tangential fields of theoretical physics and engineering. The use of fractional calculus allowed the computation of the α-order fractional derivative ζ(α). The biggest difficulty was represented by the fractional differentiation in the complex plane. In particular, two generalizations of the fractional derivative (Caputo derivative and Grünw
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Pathak, Nimishaben Shailesh. "Lyapunov-type inequality and eigenvalue estimates for fractional problems." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/dissertations/1249.

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In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.
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Bologna, Mauro. "The Dynamic Foundation of Fractal Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4235/.

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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and
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Hartter, Beverly Jo Dossey John A. "Concept image and concept definition for the topic of the derivative." Normal, Ill. Illinois State University, 1995. http://wwwlib.umi.com/cr/ilstu/fullcit?p9603516.

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Thesis (Ph. D.)--Illinois State University, 1995.<br>Title from title page screen, viewed May 2, 2006. Dissertation Committee: John A. Dossey (chair), Stephen H. Friedberg, Beverly S. Rich, Kenneth Strand, Jane O. Swafford. Includes bibliographical references (leaves 93-97) and abstract. Also available in print.
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Hejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.

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In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.
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Chalk, Carl. "Nonlinear evolutionary equations in Banach spaces with fractional time derivative." Thesis, University of Hull, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440650.

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Feng, Libo. "Numerical investigation and application of fractional dynamical systems." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/126980/1/Libo_Feng_Thesis.pdf.

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This thesis mainly concerns the numerical investigation and application of fractional dynamical systems. Two main problems are considered: fractional dynamical models involving the Riesz fractional operator, such as the time-space fractional Bloch-Torrey equation, and complex viscoelastic non-Newtonian Maxwell and Oldroyd-B fluid models. The two main contributions of the research are the treatment of the Riesz space fractional derivative on irregular convex domains and presenting a unified numerical scheme to solve a class of novel multi-term time fractional non-Newtonian fluid models. A rigor
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Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional deri
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Ito, Yu. "Rough path theory via fractional calculus." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199445.

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Malaikah, Honaida Muhammed S. "Stochastic volatility models and memory effect." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-volatility-models-and-mempry-effect(424f6c71-a0e7-44ba-afbb-cc5f74ae075c).html.

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Books on the topic "Fractional derivative"

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Chen, Wen, HongGuang Sun, and Xicheng Li. Fractional Derivative Modeling in Mechanics and Engineering. Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8802-7.

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Uchaikin, Vladimir V. Fractional Derivatives for Physicists and Engineers. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33911-0.

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Gómez, José Francisco, Lizeth Torres, and Ricardo Fabricio Escobar, eds. Fractional Derivatives with Mittag-Leffler Kernel. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11662-0.

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A, Kilbas A., and Marichev O. I, eds. Fractional integrals and derivatives: Theory and applications. Gordon and Breach Science Publishers, 1993.

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Brychkov, I︠U︡ A. Handbook of special functions: Derivatives, integrals, series, and other formulas. CRC Press, 2008.

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Brychkov, I︠U︡ A. Handbook of special functions: Derivatives, integrals, series and other formulas. CRC Press, 2008.

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Wang, JinRong, Shengda Liu, and Michal Fečkan. Iterative Learning Control for Equations with Fractional Derivatives and Impulses. Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8244-5.

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Fractional Derivative Modeling in Mechanics and Engineering. Springer, 2023.

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Fractional Derivative Modeling in Mechanics and Engineering. Springer Singapore Pte. Limited, 2022.

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Fractional-Order Integral and Derivative Operators and Their Applications. MDPI, 2020. http://dx.doi.org/10.3390/books978-3-03936-651-4.

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Book chapters on the topic "Fractional derivative"

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Milici, Constantin, Gheorghe Drăgănescu, and J. Tenreiro Machado. "Fractional Derivative and Fractional Integral." In Nonlinear Systems and Complexity. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00895-6_2.

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Zhmakin, Alexander I. "Fractional Derivative Models." In Non-Fourier Heat Conduction. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25973-9_8.

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Padula, Fabrizio, and Antonio Visioli. "Fractional-Order Proportional-Integral-Derivative Controllers." In Advances in Robust Fractional Control. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10930-5_3.

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Chen, Wen, HongGuang Sun, and Xicheng Li. "Fractal and Fractional Calculus." In Fractional Derivative Modeling in Mechanics and Engineering. Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8802-7_3.

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Georgiev, Svetlin G. "The Caputo Fractional Δ-Derivative on Time Scales." In Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73954-0_7.

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Najariyan, Marzieh, Mehran Mazandarani, and Valentina Emilia Balas. "Fuzzy Fractional Derivative: A New Definition." In Soft Computing Applications. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62524-9_25.

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Anastassiou, George A. "Fractional Left Local General M-Derivative." In Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38636-8_27.

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Anastassiou, George A. "Fractional Right Local General M-Derivative." In Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38636-8_28.

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Melliani, Said, A. Chafiki, and L. S. Chadli. "New Fractional Derivative in Colombeau Algebra." In Recent Advances in Intuitionistic Fuzzy Logic Systems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02155-9_9.

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Skovranek, Tomas, and Vladimir Despotovic. "Signal prediction using fractional derivative models." In Applications in Engineering, Life and Social Sciences, Part B, edited by Dumitru Bǎleanu and António Mendes Lopes. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571929-007.

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Conference papers on the topic "Fractional derivative"

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Nguedjio, Loic Chrislin, Rostand Moutou Pitti, Benoit Blaysat, Pierre Kisito Talla, Nicolas Sauvat, and Joseph Gril. "FRACTIONAL ORDER DERIVATIVE APPROACH OF VISCOELASTIC BEHAVIOR OF TROPICAL WOOD." In World Conference on Timber Engineering 2025. World Conference On Timber Engineering 2025, 2025. https://doi.org/10.52202/080513-0669.

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Ortigueira, Manuel D., and Juan J. Trujillo. "On a Unified Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47317.

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A new fractional derivative of complex Gru¨wald-Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Gru¨wald-Letnikov and other fractional derivatives well known. Several properties of such generalized operator are presented.
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Baleanu, Dumitru, Om P. Agrawal, and Sami I. Muslih. "Lagrangians With Linear Velocities Within Hilfer Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47953.

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Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.
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Li, Xiaorang, Christopher Essex, and Matt Davison. "A Local Fractional Derivative." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48385.

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A new definition of fractional order derivative is given and its basic properties are investigated. This definition is based on the Weyl derivative and is a local property of functions. It can be applied to non-differentiable functions and may be useful for studying fractal curves.
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Damasceno, Berenice C., and Luciano Barbanti. "Linking fractional derivative and derivative in time scales." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0042.

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Jiang, Yuehua, and HongGuang Sun. "Fractional derivative Norton–Power creep equation." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153376.

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Kuroda, Masaharu. "Fractional Derivatives and Complex Modes of Vibration." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86933.

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As described herein, we develop a method to obtain a fractional derivative response of a vibratory system with multiple degrees of freedom (DOF). To obtain fractional-order derivatives/integrals of dynamic response at a certain point on a structure presents technical difficulties because measurements of fractional-order derivative/integral responses in structural dynamics yield some implementation techniques. However, our method obviates special sensors with additional signal-conversion functions. Therefore, existing displacement and velocity sensors can work. Obtaining fractional derivative r
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Fukunaga, Masataka, Nobuyuki Shimizu, and Hiroshi Nasuno. "Fractional Derivative Consideration on Nonlinear Viscoelastic Dynamical Behavior Under Statical Pre-Displacement." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84452.

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Nonlinear fractional calculus model for the viscoelastic material is examined for oscillation around the off-equilibrium point. The model equation consists of two terms of different order fractional derivatives. The lower order derivative characterizes the slow process, and the higher order derivative characterizes the process of rapid oscillation. The measured difference in the order of the fractional derivative of the material, that the order is higher when the material is rapidly oscillated than when it is slowly compressed, is partly attributed to the difference in the frequency dependence
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Narahari Achar, B. N., Carl F. Lorenzo, and Tom T. Hartley. "Initialization Issues of the Caputo Fractional Derivative." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84348.

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The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly acc
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Lorenzo, Carl F., and Tom T. Hartley. "Initialization of Fractional Differential Equations: Background and Theory." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34810.

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It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order operators. This paper provides background on past work in the area and determines the Laplace transforms for initialized fractional integrals of any order and fractional derivatives of order less than one. A companion paper in this conference extends the theo
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Reports on the topic "Fractional derivative"

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Charusiri, Punya, Wasant Pongsapich, and Chakkaphan Sutthirat. Petrochemistry of probable gem-bearing basalts in Sop Prap-Ko Kha Area, Changwat Lampang : research report. Chulalongkorn University, 1996. https://doi.org/10.58837/chula.res.1996.17.

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The project area covers approximately 300 km[superscript 2] encompassing parts of Amphoe Sop Prap, Amphoe Ko Kha, and Amphoe Mae Tha of Changwat Lampang. The area is mainly occupied by sedimentary (and metamorphic) rocks of Permian, Triassic, Tertiary and Quaternary ages. The Triassic rocks include the Phra That, the Pha Kan, and the Hong Hoi Formations of the Lampang Group. Igneous rocks comprise Permo-Triassic volcanics, Triassic granodiorite, and Cenozoic basalts. Sapphires are frequently found in alluvial and residual deposits, particularly in the northern basaltic area. Sapphires in the s
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