Relevant bibliographies by topics / Derivative calculus

Contents

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

Academic literature on the topic 'Derivative calculus'

Author: Grafiati
Published: 7 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Derivative calculus"

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Deppman, Airton, Eugenio Megías, and Roman Pasechnik. "Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus." Entropy 25, no. 7 (2023): 1008. http://dx.doi.org/10.3390/e25071008.

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This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the q-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A sim
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Martínez, Francisco, and Mohammed K. A. Kaabar. "A New Generalized Definition of Fractal–Fractional Derivative with Some Applications." Mathematical and Computational Applications 29, no. 3 (2024): 31. http://dx.doi.org/10.3390/mca29030031.

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In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function’s derivative. We complete the theory of generalized FF calculus by proposing a notion of integr
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Hariharan, Ramaraj, and Ramalingam Udhayakumar. "Existence of mild solution for fuzzy fractional differential equation utilizing the Hilfer-Katugampola fractional derivative." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 15, no. 1 (2025): 80. https://doi.org/10.36922/ijocta.1653.

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This paper explores the existence of mild solutions for fuzzy fractional differential equations involving the Hilfer-Katugampola fractional derivative. This derivative generalizes classical fractional derivatives, such as the Riemann- Liouville and Hadamard derivatives, offering a broader framework for fractional calculus. The existence conditions for mild solutions are established using fractional calculus, semigroup theory, and Schauder’s fixed point theorem. An example is provided to demonstrate the theoretical applications of the main results.
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Ortigueira, Manuel D., and Gary W. Bohannan. "Fractional Scale Calculus: Hadamard vs. Liouville." Fractal and Fractional 7, no. 4 (2023): 296. http://dx.doi.org/10.3390/fractalfract7040296.

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A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. For solving the corresponding differential equations, a new logarithmic Mittag-Leffler series is proposed.
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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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Farid, Ghulam, and Zeeshan Afzal. "Further on quantum-plank derivatives and integrals in composite forms." Open Journal of Mathematical Analysis 6, no. 2 (2022): 130–38. http://dx.doi.org/10.30538/psrp-oma2022.0118.

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In quantum-plank calculus, q-derivatives and h-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called q−h-derivative. This paper aims to present a further generalized notion of derivatives will be called (q ,p−h)-derivatives. This will produce q-derivative, h-derivative, q−h-derivative and (p,q)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.
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M. Alawaideh, Yazen, Aysel Ramazanova, Hayat Issaadi, Bashar M. Al-khamiseh, Muhammad Bilal, and Dumitru Baleanu Baleanu. "Generalized Conformable Hamiltonian Dynamics with Higher-Order Derivatives." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5478. https://doi.org/10.29020/nybg.ejpam.v18i1.5478.

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In this paper, we investigate higher-order calculus using the conformable derivative and integral. We use a fractional variant of the calculus of variations to obtain the Euler-Lagrange equation. Our route integral quantization approach streamlines the procedure by integrating solely over canonical coordinates q, eliminating the requirement to integrate higher-order derivatives . In addition, we employ the conformable derivative to develop canonical conserved energy-momentum and Ostrogradsky’s Hamiltonian. Furthermore, we generalized the Hamilton formulation for higher order derivatives and ap
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Karim, Avin O., Enas M. Shehata, and José Luis Cardoso. "The Directional Derivative in General Quantum Calculus." Symmetry 14, no. 9 (2022): 1766. http://dx.doi.org/10.3390/sym14091766.

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In this paper, we define the β-partial derivative as well as the β-directional derivative of a multi-variable function based on the β-difference operator, Dβ, which is defined by Dβf(t)=f(β(t))−f(t)/β(t)−t, where β is a strictly increasing continuous function. Some properties are proved. Furthermore, the β-gradient vector and the β-gradient directional derivative of a multi-variable function are introduced. Finally, we deduce the Hahn-partial and the Hahn-directional derivatives associated with the Hahn difference operator.
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Çakmak, Serkan. "Complex deformable calculus." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 2 (2024): 486–95. http://dx.doi.org/10.31801/cfsuasmas.1377811.

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In this paper, we give a new complex deformable derivative and integral of order λ which coincides with the classical derivative and integral for the special values of the parameters. We examine the basic properties of this derivative and integral. We also investigate the basic concepts of complex analysis for the λ-complex deformable derivative. Finally, we give some applications.
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Dissertations / Theses on the topic "Derivative calculus"

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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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Hyer, Charity Ann. "Discovering the derivative can be "invigorating" : Mark's journey to understanding instantaneous velocity /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2048.pdf.

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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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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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Mattos, William Febronio de. "Uma contribuição para o ensino de cálculo no ensino médio, utilizando a classe das cônicas." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-06042016-094506/.

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O Cálculo Diferencial e Integral é o ramo da matemática no qual um dos objetivos é o estudo do movimento e da variação. Desenvolvido a partir da Álgebra e da Geometria, esse ramo dedica-se ao estudo de taxas de variação de grandezas, como a inclinação de uma reta tangente a uma curva em um dos seus pontos, e a acumulação de quantidades, como a área sob uma curva e o volume de um sólido. Por ser utilizado como uma ferramenta auxiliar em várias áreas das ciências pura e aplicada e, dada a sua aplicabilidade nas mais diversas áreas do conhecimento, é considerado um dos conteúdos mais importantes
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Bansilal, S., and E. Pillay. "An exploration of Grade 12 learners' use of inappropriate algorithms in calculus." Journal for New Generation Sciences, Vol 12, Issue 2: Central University of Technology, Free State, Bloemfontein, 2014. http://hdl.handle.net/11462/657.

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Published Article<br>This study was conducted with 29 Grade 12 learners who were studying calculus. The purpose was to explore how the learners responded to questions based on the derivative and why they did so. Data was collected from the written responses of the learners to two assessments carried out over a six-month period as well as interviews with four of the learners. It was found that learners made extensive use of inappropriate formulae, drawn from other sections of the curriculum The study recommends that teachers should not focus solely on how to carry out procedures, but they shoul
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Hyer, Charity Ann Gardner. "Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/1173.

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This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark's sense making of the derivative is analyzed in light of his use
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Rachelli, Janice. "COMPREENSÃO DOS CONCEITOS DE DERIVADA CLÁSSICA E DERIVADA FRACA: ANÁLISE SEGUNDO O MODELO COGNITIVO APOS." Centro Universitário Franciscano, 2017. http://www.tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/601.

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Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T17:53:01Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_JaniceRachelli.pdf: 4818944 bytes, checksum: 0c02a81d2b4c04364b21e1ddddc2fe58 (MD5)<br>Made available in DSpace on 2018-08-20T17:53:01Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_JaniceRachelli.pdf: 4818944 bytes, checksum: 0c02a81d2b4c04364b21e1ddddc2fe58 (MD5) Previous issue date: 2017-10-03<br>The present study is on the field of Mathematics Education in highe
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Amsheri, Somia Muftah Ahmed. "Fractional calculus operator and its applications to certain classes of analytic functions : a study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and ρ-valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of ρ-valent functions with negative coefficients in the open unit disk such as classes of ρ-valent starlike f
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Amsheri, Somia M. A. "Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of -valent functions with negative coefficients in the open unit disk such as classes of -valent starlike func
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Books on the topic "Derivative calculus"

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1968-, Rennie Andrew, ed. Financial calculus: An introduction to derivative pricing. Cambridge University Press, 1996.

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Penot, Jean-Paul. Calculus Without Derivatives. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4538-8.

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Penot, Jean-Paul. Calculus Without Derivatives. Springer New York, 2013.

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Horacio, Porta, and Uhl J. J, eds. Calculus&Mathematica: Derivatives : measuring growth. Addison-Wesley, 1994.

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Garg, Krishna M. Theory of differentiation: A unified theory of differentiation via new derivate theorems and new derivatives. Wiley, 1998.

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Manichev, Vladimir, Valentina Glazkova, and Кузьмина Анастасия. Numerical methods. The authentic and exact solution of the differential and algebraic equations in SAE systems of SAPR. INFRA-M Academic Publishing LLC., 2016. http://dx.doi.org/10.12737/13138.

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In the manual classical numerical methods are considered&#x0D; and algorithms for the decision of systems of the ordinary differential&#x0D; equations (ODE), nonlinear and linear algebraic equations&#x0D; (NAU and LAU), and also ways of ensuring reliability and demanded&#x0D; accuracy of results of the decision. Ideas, which still not are stated&#x0D; are reflected in textbooks on calculus mathematics, namely: decision&#x0D; systems the ODE without reduction to a normal form of Cauchy resolved&#x0D; rather derivative, and refusal from any numerical an equivalent -&#x0D; nykh of transformations
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1947-, Guzman Alberto. Derivatives and integrals of multivariable functions. Birkhauser, 2003.

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E, Ward James, and Anton Howard, eds. The calculus companion to accompany Calculus, Howard Anton, third edition: Review prroblems in derivatives. Wiley, 1987.

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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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Book chapters on the topic "Derivative calculus"

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Kac, Victor, and Pokman Cheung. "q-Derivative and h-Derivative." In Quantum Calculus. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_1.

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Callahan, James J. "The Derivative." In Advanced Calculus. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7332-0_4.

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Rogawski, Jon, and Colin Adams. "Applications of the Derivative." In Calculus. Macmillan Learning, 2015. http://dx.doi.org/10.1007/978-1-319-16793-6_4.

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Kac, Victor, and Pokman Cheung. "h-Derivative and h-Integral." In Quantum Calculus. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_22.

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Ghergu, Marius. "Directional Derivative." In Differential Calculus in Several Variables. Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003449652-6.

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Thompson, Silvanus P., and Martin Gardner. "What Is a Derivative?" In Calculus Made Easy. Macmillan Education UK, 1998. http://dx.doi.org/10.1007/978-1-349-15058-8_3.

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Lax, Peter D., and Maria Shea Terrell. "The Derivative and Differentiation." In Calculus With Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7946-8_3.

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Lax, Peter D., and Maria Shea Terrell. "Applications of the Derivative." In Calculus With Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7946-8_5.

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Pfaff, Thomas J. "The Derivative Graphically." In Applied Calculus with R. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28571-4_9.

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Pfaff, Thomas J. "Basic Derivative Rules." In Applied Calculus with R. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28571-4_11.

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Conference papers on the topic "Derivative calculus"

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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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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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Agrawal, Om P., Md Mehedi Hasan, and X. W. Tangpong. "A Numerical Scheme for a Class of Parametric Problem of Fractional Variational Calculus." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48768.

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Fractional derivatives (FDs) or derivatives of arbitrary order have been used in many applications, and it is envisioned that in future they will appear in many functional minimization problems of practical interest. Since fractional derivatives have such property as being non-local, it can be extremely challenging to find analytical solutions for fractional parametric optimization problems, and in many cases, analytical solutions may not exist. Therefore, it is of great importance to develop numerical methods for such problems. This paper presents a numerical scheme for a linear functional mi
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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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Abu-Alshaikh, Ibrahim, Anas N. Al-Rabadi, and Hashem S. Alkhaldi. "Dynamic Response of a Beam With Absorber Exposed to a Running Force: Fractional Calculus Approach." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-93178.

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This paper analyzes the transverse vibration of Bernoulli-Euler homogeneous isotropic simply-supported beam. The beam is assumed to be fractionally-damped and attached to a single-degree-of-freedom (SDOF) absorber with fractionally-damping behavior at the mid-span of the beam. The beam is also exposed to a running force with constant velocity. The fractional calculus is introduced to model the damping characteristics of both the beam and absorber. The Laplace transform accompanied by the used decomposition method is applied to solve the handled problem with homogenous initial conditions. Subse
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Xavier, Paulo Henrique Farias. "FRACTIONAL CALCULUS: AN APPROACH TO THE ATMOSPHERICDISPERSION EQUATION USING CONFORMABLE DERIVATIVE." In VI Simpósio Internacional de Inovação e Tecnologia. Editora Blucher, 2020. http://dx.doi.org/10.5151/siintec2020-fractionalcalculus.

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Hong, Dae. "How Do College Calculus Instructors Solve and Potentially Teach Derivative Graphs?" In AERA 2023. AERA, 2023. http://dx.doi.org/10.3102/ip.23.2001395.

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Saepuzaman, Duden, Aldi Zulfikar, and Denni Y. Girsang. "Correlation between Students' Understanding on Derivative and Integral Calculus with Thermodynamics." In International Conference on Mathematics and Science Education. Atlantis Press, 2017. http://dx.doi.org/10.2991/icmsed-16.2017.47.

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Liu, Yaqing, Liancun Zheng, Xinxin Zhang, and Fenglei Zong. "The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22278.

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In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and
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Rabius Sunny, M. Mohammed, Rakesh K. Kapania, Ronald D. Moffitt, Amitabh Mishra, and Nakhiah Goulbourne. "A Modified Fractional Derivative Approach to Model Hysteresis." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43747.

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This paper describes the development of a fractional calculus approach to model the hysteretic behavior shown by the variation of resistance with strain in nano-composites (like MetalRubberOˆ). Experiments have been carried out on MetalRubberOˆ to study the strain-resistance variation of this material under strains varying in a triangular manner. Combined fractional derivative and integer order integral model and fractional integral model (with two sub-models) have been developed to model this behavior. Effieiency of these models has been discussed by comparison of their results with the exper
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Reports on the topic "Derivative calculus"

1

Basta, Oussama. Modular Calculus: A Fundamental Framework for Cyclic Derivatives and the Absolute Unified Theory. ResearchHub Technologies, Inc., 2025. https://doi.org/10.55277/researchhub.zg03pxwf.1.

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