Relevant bibliographies by topics / Caputo derivatives

Contents

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

Academic literature on the topic 'Caputo derivatives'

Author: Grafiati
Published: 28 June 2021
Last updated: 29 July 2025

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Journal articles on the topic "Caputo 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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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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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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Peng, Zhongqi, Yuan Li, Qi Zhang, and Yimin Xue. "Extremal Solutions for Caputo Conformable Differential Equations with p-Laplacian Operator and Integral Boundary Condition." Complexity 2021 (October 25, 2021): 1–14. http://dx.doi.org/10.1155/2021/1097505.

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The Caputo conformable derivative is a new Caputo-type fractional differential operator generated by conformable derivatives. In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. We also establish two comparison principles and prove the extremal solutions for nonlinear fractional p -Laplacian differential system with Caputo conformable derivatives by utilizing the monotone iterative technique. An example is given to verify the validity of the results
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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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Tapé, Z. Grace Espérance Z., Mouhamadou Dosso, and Seydou Traoré. "On Numerical Schemes for Solving Fractional Advection-diffusion Equations in the Sense of Caputo." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 20 (July 23, 2025): 305–28. https://doi.org/10.37394/23203.2025.20.34.

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This paper presents the application of concentration described by the fractional advection-diffusion equation, considering fractional derivatives in the sense of Caputo and a new modified fractional derivative also in the sense of Caputo. Specifically, approximations of fractional derivatives of order α (m−1≤α≤m, m∈N ∗ ) using the finite difference method in the two aforementioned cases have enabled us to develop numerical resolution schemes. The results of comparative numerical tests between the two schemes showed that, with the modified Caputo derivative, diffusion is slightly faster with a
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Diethelm, Kai, Roberto Garrappa, Andrea Giusti, and Martin Stynes. "Why fractional derivatives with nonsingular kernels should not be used." Fractional Calculus and Applied Analysis 23, no. 3 (2020): 610–34. http://dx.doi.org/10.1515/fca-2020-0032.

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AbstractIn recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will be shown here, through rigorous mathematical reasoning, that these non-singular kernel derivatives suffer from several drawbacks which should forbid their use. They fail to satisfy the fundamental theorem of fractional calculus since they do not admit the existence of a corresponding convolution integral of which the derivative is the left
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Rosales García, J. Juan, J. David Filoteo, and Andrés González. "A comparative analysis of the RC circuit with local and non-local fractional derivatives." Revista Mexicana de Física 64, no. 6 (2018): 647. http://dx.doi.org/10.31349/revmexfis.64.647.

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This work is devoted to investigate solutions to RC circuits using four different types of time fractional diferential operators of order 0 < γ ≤ 1. The fractional derivatives considered are, Caputo, Caputo-Fabrizio, Atangana-Baleanu and the conformable derivative. It is shown that Atangana-Baleanu fractional derivative (non-local), and the conformable (local) derivative could describe a wider class of physical processes then the Caputo and Caputo-Fabrizio. The solutions are exactly equal for all four erivatives only for the case γ=1.
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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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Dissertations / Theses on the topic "Caputo derivatives"

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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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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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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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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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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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Kadlčík, Libor. "Efektivní použití obvodů zlomkového řádu v integrované technice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-432494.

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Integrace a derivace jsou obvykle známy pro celočíselný řád (tj. první, druhý, atd.). Existuje ale zobecnění pro zlomkové (neceločíselné) řády, které lze implementovat pomocí elektronických obvodů zlomkového řádu (případně provést jejich aproximaci) a které poskytuje nový stupeň volnosti pro návrh elektronických obvodů. Obvody zlomkového řádu jsou obvykle aproximovány diskrétními součástkami pomocí RC struktur s velkými rozsahy odporů a kapacit, a tím se jeví nepraktické pro použití v integrovaných obvodech. Tato práce prezentuje implementaci obvodů zlomkového řádu v integerovaných obvodech a
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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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Book chapters on the topic "Caputo derivatives"

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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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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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Fedorov, Vladimir E., and Kseniya V. Boyko. "Some Classes of Quasilinear Equations with Gerasimov—Caputo Derivatives." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28505-9_1.

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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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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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Oliva-Sanchez, Pedro, Ruben Aguilar-Marquez, Javier Alejandro Pérez-Garza, Edelmiro Leal-Fernandez, and Servando Lopez-Aguayo. "Analysis of the Fractional Schrödinger Equation with Free Particle Potential in One Dimension with Caputo and Caputo-Fabrizio Derivatives." In Modeling and Optimization in Science and Technologies. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-83989-4_10.

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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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Conference papers on the topic "Caputo derivatives"

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Nisardi, Muhammad Rifki, Hartina Husain, Kusnaeni, Muh Ikhsan Amar, Muh Fadhil Nurahmad, and Nur Rahmi. "A Fractional Mathematical Model of Influenza: Meningitis Coinfection Using Caputo Derivatives." In Borneo International Conference. SCITEPRESS - Science and Technology Publications, 2024. https://doi.org/10.5220/0013214100004605.

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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. "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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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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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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Reports on the topic "Caputo derivatives"

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McKean, Adam P., and Zachary W. Anderson. Interim Geologic Map of the Salt Lake City North Quadrangle, Salt Lake and Davis Counties, Utah. Utah Geological Survey, 2024. http://dx.doi.org/10.34191/ofr-768dm.

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The Salt Lake City North 7.5′ quadrangle is located in Salt Lake and Davis Counties from downtown Salt Lake City on the east to the Salt Lake International Airport on the west and extends north into Davis County to include the southern parts of the City of Bountiful and City of Woods Cross. The southern boundary of the quadrangle is at approximately 900 South Street in Salt Lake City. The quadrangle contains downtown Salt Lake City, the State Capitol building, the City of North Salt Lake, agricultural land, a number of oil refineries, a part of the Farmington Bay Waterfowl Management Area, and
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