Academic literature on the topic 'Caputo fractional derivatives'

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Journal articles on the topic "Caputo fractional derivatives"

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Li, Changpin, Deliang Qian, and YangQuan Chen. "On Riemann-Liouville and Caputo Derivatives." Discrete Dynamics in Nature and Society 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/562494.

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Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in sc
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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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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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Agarwal, Ravi, Snezhana Hristova, and Donal O’Regan. "Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability." Mathematics 10, no. 13 (2022): 2315. http://dx.doi.org/10.3390/math10132315.

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The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics, chemistry, biology, etc. In this paper, the presence of noninstantaneous impulses in differential equations with generalized proportional Caputo fractional derivatives is discussed. Generalized proportional Caputo fractional derivatives with fixed lower limits at the initial time as well as generalized proportional Caputo fractional derivatives
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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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Oliveira, Daniela S., and Edmundo Capelas de Oliveira. "On a Caputo-type fractional derivative." Advances in Pure and Applied Mathematics 10, no. 2 (2019): 81–91. http://dx.doi.org/10.1515/apam-2017-0068.

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Abstract In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order an
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Aljhani, Sami, Mohd Salmi Md Noorani, Khaled M. Saad, and A. K. Alomari. "Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott." Journal of Function Spaces 2021 (July 19, 2021): 1–12. http://dx.doi.org/10.1155/2021/2544688.

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A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional Gray-Scott model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives. We utilize the fractional homotopy analysis transformation method to obtain approximate solutions for the time-fractional Gray-Scott model. This method gives a more realistic series of solutions that converge rapidly to the exact solution. We can ensure convergence by solving the series resultant. We study the convergence analysis of fractional homot
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Agarwal, Ravi P., Snezhana Hristova, and Donal O’Regan. "Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations." Fractal and Fractional 7, no. 1 (2023): 80. http://dx.doi.org/10.3390/fractalfract7010080.

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In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of derivative generalizes several known types in the literature for fractional derivatives such as the Caputo fractional derivative. Thus, the obtained results additionally generalize some known models in the literature. The long term behavior of the solution of the model when the time is increasing without a bound is studied and sufficient conditio
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Sami, Ahmed, and Sameer Qasim Hasan. "Stability of Composition Caputa– Katugampola Fractional Differential Nonlinear Control System with Delay Riemann −Katugampola." Mustansiriyah Journal of Pure and Applied Sciences 2, no. 4 (2024): 19–40. http://dx.doi.org/10.47831/mjpas.2024.2.4.19-40.

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work used the Composition Caputo-Katugampola Fractional Derivatives technique to tackle nonlinear problems and delay fractional differential equations. The fractional derivative is defined using the Caputo and Riemann-Katugampola Fractional Derivatives Method. Proposed method In comparison to other digital technologies, this one is simple, effective, and uncomplicated. Ensure authenticity and correctness proposed method Some exemplary problems have been solved
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Sami, Ahmed, and Sameer Qasim Hasan. "Stability of Composition Caputa– Katugampola Fractional Differential Nonlinear Control System with Delay Riemann −Katugampola." Mustansiriyah Journal of Pure and Applied Sciences 2, no. 4 (2024): 19–40. http://dx.doi.org/10.47831/mjpas.v2i4.131.

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work used the Composition Caputo-Katugampola Fractional Derivatives technique to tackle nonlinear problems and delay fractional differential equations. The fractional derivative is defined using the Caputo and Riemann-Katugampola Fractional Derivatives Method. Proposed method In comparison to other digital technologies, this one is simple, effective, and uncomplicated. Ensure authenticity and correctness proposed method Some exemplary problems have been solved
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Dissertations / Theses on the topic "Caputo fractional derivatives"

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Teodoro, Graziane Sales 1990. "Cálculo fracionário e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306995.

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Orientador: Edmundo Capelas de Oliveira<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T12:52:57Z (GMT). No. of bitstreams: 1 Teodoro_GrazianeSales_M.pdf: 8150080 bytes, checksum: 07ef5ddebc25d941750b2dee59bd4022 (MD5) Previous issue date: 2014<br>Resumo: O cálculo fracionário, nomenclatura utilizada para cálculo de ordem não inteira, tem se mostrado importante e, em muitos casos, imprescindível na discussão de problemas advindos de diversas áreas da ciência, como na matemátic
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Oliveira, Daniela dos Santos de 1990. "Derivada fracionária e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306994.

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Orientador: Edmundo Capelas de Oliveira<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T00:53:38Z (GMT). No. of bitstreams: 1 Oliveira_DanieladosSantosde_M.pdf: 3702602 bytes, checksum: c0b05792ff3ac3c5bdd5fad1b7586dd5 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho apresentamos um estudo sobre as funções de Mittag-Leffler de um, dois e três parâmetros. Apresentamos a função de Mittag-Leffler como uma generalização da função exponencial bem como a relação que esta po
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Oti, Vincent Bediako. "Numerické metody pro řešení počátečních úloh zlomkových diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445462.

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Tato diplomová práce se zabývá numerickými metodami pro řešení počátečních problémů zlomkových diferenciálních rovnic s Caputovou derivací. Jsou uvedeny dva numerické přístupy spolu s přehledem základních aproximačních formulí. Dvě verze Eulerovy metody jsou realizovány v Matlabu a porovnány na základě numerických experimentů.
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Kárský, Vilém. "Modelování LTI SISO systémů zlomkového řádu s využitím zobecněných Laguerrových funkcí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316278.

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This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.
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BUCUR, CLAUDIA DALIA. "Some nonlocal operators and effects due to nonlocality." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/10281/277792.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive introduction to the fractional Laplacian, we present some related contemporary research results and we add some original material. Indeed, we study the potential theory of this operator, introduce a new proof of Schauder estimates using the potential theory approach, we study a fractional elliptic problem in Rn with convex nonlinearities and critical growth and we presen
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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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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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Bucur, C. D. "SOME NONLOCAL OPERATORS AND EFFECTS DUE TO NONLOCALITY." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/488032.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and some other types of fractional derivatives. We make an extensive introduction to the fractional Laplacian and to some related contemporary research themes. We add to this some original material: the potential theory of this operator and a proof of Schauder estimates with the potential theory approach, the study of a fractional elliptic problem in $mathbb{R}^n$ with convex nonlinearities and critical growth, and a stickiness property of $s$-minimal surfaces as $s$ gets small. Also,
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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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Hnaien, Dorsaf. "Equations aux dérivées fractionnaires : propriétés et applications." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS038.

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Notre objectif dans cette thèse est l'étude des équations différentielles non linéaires comportant des dérivées fractionnaires en temps et/ou en espace. Nous nous sommes intéressés dans un premier temps à l'étude de deux systèmes non linéaires d'équations différentielles fractionnaires en temps et/ou en espace, puis à l'étude d'une équation différentielle fractionnaire en temps. Plus exactement pour la première partie, les questions concernant l'existence globale et le comportement asymptotique des solutions d'un système non linéaire d'équations différentielles comportant des dérivées fraction
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Book chapters on the topic "Caputo fractional derivatives"

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Almeida, Ricardo, Agnieszka B. Malinowska, and Delfim F. M. Torres. "Fractional Euler–Lagrange Differential Equations via Caputo Derivatives." In Fractional Dynamics and Control. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0457-6_9.

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Anastassiou, George A., and Ioannis K. Argyros. "Iterative Algorithms and Left-Right Caputo Fractional Derivatives." In Intelligent Numerical Methods: Applications to Fractional Calculus. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-26721-0_14.

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Agarwal, Ravi, Snezhana Hristova, and Donal O’Regan. "Non-instantaneous Impulses in Differential Equations with Caputo Fractional Derivatives." In Non-Instantaneous Impulses in Differential Equations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66384-5_2.

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Akdemir, Ahmet Ocak, Hemen Dutta, Ebru Yüksel, and Erhan Deniz. "Inequalities for m-Convex Functions via Ψ-Caputo Fractional Derivatives." In Mathematical Methods and Modelling in Applied Sciences. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43002-3_17.

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Chikrii, Arkadii, and Ivan Matychyn. "Riemann–Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games." In Annals of the International Society of Dynamic Games. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-8089-3_4.

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Ahmad, Bashir, Ahmed Alsaedi, Sotiris K. Ntouyas, and Jessada Tariboon. "Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives." In Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52141-1_7.

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Mahatekar, Yogita, and Pallavi S. Scindia. "Numerical Methods for Solving Fractional Differential Equations in Terms of Caputo-Fabrizio and Proportional Caputo Derivatives." In Studies in Systems, Decision and Control. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-84955-8_7.

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D’Abbicco, Marcello. "Critical Exponents for Differential Inequalities with Riemann-Liouville and Caputo Fractional Derivatives." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10937-0_2.

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Lavín-Delgado, J. E., J. E. Solís-Pérez, J. F. Gómez-Aguilar, and R. F. Escobar-Jiménez. "Image Edge Detection Using Fractional Conformable Derivatives in Liouville-Caputo Sense for Medical Image Processing." In Fractional Calculus in Medical and Health Science. CRC Press, 2020. http://dx.doi.org/10.1201/9780429340567-1.

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Balcázar-Araiza, Roberto Carlos, and José Matías Navarro-Soza. "A Fundamental Theorem of Curves in the Euclidean Space with Caputo Fractional Derivatives." In Modeling and Optimization in Science and Technologies. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-83989-4_1.

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Conference papers on the topic "Caputo fractional derivatives"

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Lv, Yan, Yuanquan Liu, Qiang Shao, Yan Yu, and Yan Liu. "Fractional Order Gradient Descent with Caputo Derivatives for Product-Unit Neural Networks." In 2025 8th International Conference on Advanced Algorithms and Control Engineering (ICAACE). IEEE, 2025. https://doi.org/10.1109/icaace65325.2025.11020545.

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Adebisi, Ajimot F., Gbolahan M. Gbolagade, Muideen O. Ogunniran, Ezekiel Olaoluwa Omole, Femi Emmanuel Amoyedo, and Kehinde Peter Ajewole. "Convergence and Stability Analysis of Finite Difference Methods, Caputo Derivatives, and Collocation Methods Applied to Space Fractional Diffusion Equations." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10630199.

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Naifar, Omar. "Practical Observer Design for Nonlinear Systems using Caputo Fractional Derivative with Respect to Another Function." In 2025 IEEE 22nd International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, 2025. https://doi.org/10.1109/ssd64182.2025.10989893.

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Baleanu, Dumitru, Sami I. Muslih, and Eqab M. Rabei. "On Fractional Hamilton Formulation Within Caputo Derivatives." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34812.

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The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristi
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Baleanu, Dumitru. "On Constrained Systems Within Caputo Derivatives." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35009.

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The constraints systems play a very important role in physics and engineering. The fractional variational principles were successfully applied to control problems as well as to construct the phase space of a fractional dynamical system. In this paper the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase-space is analyzed. One system possessing two primary first class constraints is analyzed in detail.
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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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Trigeassou, Jean-Claude, Nezha Maamri, and Alain Oustaloup. "Initialization of Riemann-Liouville and Caputo Fractional Derivatives." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47633.

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Riemann-Liouville and Caputo fractional derivatives are fundamentally related to fractional integration operators. Consequently, the initial conditions of fractional derivatives are the frequency distributed and infinite dimensional state vector of fractional integrators. The paper is dedicated to the estimation of these initial conditions and to the validation of the initialization problem based on this distributed state vector. Numerical simulations applied to Riemann-Liouville and Caputo derivatives demonstrate that the initial conditions problem can be solved thanks to the estimation of th
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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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Ortigueira, Manuel D. "On the “walking dead” derivatives: Riemann-Liouville and Caputo." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967433.

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Biswas, Raj Kumar, and Siddhartha Sen. "Numerical Method for Solving Fractional Optimal Control Problems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87008.

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A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from t
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