Relevant bibliographies by topics / Fractional calculus

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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 calculus'

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

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Journal articles on the topic "Fractional calculus"

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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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Baleanu, Dumitru. "About Fractional Calculus of Singular Lagrangians." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 4 (2005): 395–98. http://dx.doi.org/10.20965/jaciii.2005.p0395.

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In this paper the solutions of the fractional Euler-Lagrange quations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.
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Zhao, Yan Chun. "Design and Application of Digital Filter Based on Calculus Computing Concept." Applied Mechanics and Materials 513-517 (February 2014): 3151–55. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.3151.

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Calculus has been widely applied in engineering fields. The development of Integer order calculus theory is more mature in the project which can obtain fractional calculus theory through the promotion of integration order. It extends the flexibility of calculation and achieves the engineering analysis of multi-degree of freedom. According to fractional calculus features and the characteristics of fractional calculus, this paper treats the frequency domain as the object of study and gives the fractional calculus definition of the frequency characteristics. It also designs the mathematical model
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Chii-Huei, Yu. "Using Integration by Parts for Fractional Calculus to Solve Some Fractional Integral Problems." International Journal of Electrical and Electronics Research 11, no. 2 (2023): 1–5. https://doi.org/10.5281/zenodo.7830903.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we solve some fractional integrals by using integration by parts for fractional calculus. A new multiplication of fractional analytic functions plays an important role in this article. In fact, our results are generalizations of traditional calculus results. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, fractional integrals, integration by parts for fractional calculus, new multiplication, fractional analytic functions. <strong>Title:</strong> Using Integration
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Chii-Huei, Yu. "An Improper Fractional Integral Involving Fractional Exponential Function." International Journal of Recent Research in Mathematics Computer Science and Information Technology 10, no. 1 (2023): 57–61. https://doi.org/10.5281/zenodo.8248860.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we use integration by parts for fractional calculus to solve an improper fractional integral involving fractional exponential function. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, integration by parts for fractional calculus, improper fractional integral, fractional exponential functi
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Chii-Huei, Yu. "A Study of Two Fractional Integral Problems Based on Jumarie Type of Riemann-Liouville Fractional Calculus." International Journal of Civil and Structural Engineering Research 12, no. 2 (2024): 15–19. https://doi.org/10.5281/zenodo.13982262.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we find the exact solutions of two fractional integrals. Integration by parts for fractional calculus and a new multiplication of fractional analytic functions play important roles in this article. In fact, our results are generalizations of classical calculus results.&nbsp; <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, fractional integrals, integration by parts for fractional calculus, new multiplication, fractional analytic functions. <strong>Title:</strong> A
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Chii-Huei, Yu, and Yang Kuang-Wu. "Solving Some Type of Improper Fractional Integral Using Differentiation under Fractional Integral Sign and Integration by Parts for Fractional Calculus." International Journal of Engineering Research and Reviews 12, no. 4 (2024): 34–38. https://doi.org/10.5281/zenodo.13939320.

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<strong>Abstract: </strong>In this paper, based on Jumarie&rsquo;s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study some type of improper fractional integral. We can obtain the exact solution of this improper fractional integral by using differentiation under fractional integral sign and integration by parts for fractional calculus. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie&rsquo;s modified R-L fractional calculus, new multiplication, fractional analytic functi
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Sabzikar, Farzad, Mark M. Meerschaert, and Jinghua Chen. "Tempered fractional calculus." Journal of Computational Physics 293 (July 2015): 14–28. http://dx.doi.org/10.1016/j.jcp.2014.04.024.

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Lubich, Ch. "Discretized Fractional Calculus." SIAM Journal on Mathematical Analysis 17, no. 3 (1986): 704–19. http://dx.doi.org/10.1137/0517050.

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Tarasov, Vasily E. "Lattice fractional calculus." Applied Mathematics and Computation 257 (April 2015): 12–33. http://dx.doi.org/10.1016/j.amc.2014.11.033.

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Dissertations / Theses on the topic "Fractional calculus"

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Tavares, Dina dos Santos. "Fractional calculus of variations." Doctoral thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22184.

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Doutoramento em Matemática e Aplicações<br>O cálculo de ordem não inteira, mais conhecido por cálculo fracionário, consiste numa generalização do cálculo integral e diferencial de ordem inteira. Esta tese é dedicada ao estudo de operadores fracionários com ordem variável e problemas variacionais específicos, envolvendo também operadores de ordem variável. Apresentamos uma nova ferramenta numérica para resolver equações diferenciais envolvendo derivadas de Caputo de ordem fracionária variável. Consideram- -se três operadores fracionários do tipo Caputo, e para cada um deles é apresentad
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Kimeu, Joseph M. "Fractional Calculus: Definitions and Applications." TopSCHOLAR®, 2009. http://digitalcommons.wku.edu/theses/115.

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McBride, Adam C. "Fractional calculus, fractional powers of operators and Mellin multiplier transforms." Thesis, University of Edinburgh, 1994. http://hdl.handle.net/1842/15310.

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We shall present a theory of fractional calculus for generalised functions on (0,∞) and use this theory as a basis for extensions to some related areas. In the first section, appropriate spaces of test-functions and generalised functions on (0,∞) are introduced and the properties of operators of fractional calculus obtained relative to these spaces. Applications are given to hypergeometric integral equations, Hankel transforms and dual integral equations of Titchmarsh type. In the second section, the Mellin transform is used to define fractional powers of a very general class of operators. The
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Ferreira, Rui Alexandre Cardoso. "Calculus of variations on time scales and discrete fractional calculus." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/2921.

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Doutoramento em Matemática<br>Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fr
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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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Waddell, Chris. "Fractional calculus and scales of spaces." Thesis, University of Strathclyde, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288637.

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Abdelsheed, Ismail Gad Ameen. "Fractional calculus: numerical methods and SIR models." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3422267.

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Fractional calculus is ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. The idea of generalizing differential operators to a non-integer order, in particular to the order 1/2, first appears in the correspondence of Leibniz with L’Hopital (1695), Johann Bernoulli (1695), and John Wallis (1697) as a mere question or maybe even play of thoughts. In the following three hundred years a lot of mathematicians contributed to the fractional calculus: Laplace (1812), Lacroix (1812), Fourier (1822
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Shen, Xin. "Applications of Fractional Calculus In Chemical Engineering." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37577.

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Fractional calculus, which is a generalization of classical calculus, has been the subject of numerous applications in physics and engineering during the last decade. In this thesis, fractional calculus has been implemented for chemical engineering applications, namely in process control and in the modeling mass transfer in adsorption. With respect to process control, some researchers have proposed fractional PIλDμ controllers based on fractional calculus to replace classical PI and PID controllers. The closed-loop control of different benchmark dynamic systems using optimally-tuned fraction
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Sikaneta, Ishuwa Christopher. "From fractional calculus to split dimensional regularization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0012/MQ31867.pdf.

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Beig, Mirza Tanweer Ahmad. "Fractional Calculus and Dynamic Approach to Complexity." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc822832/.

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Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automat
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Books on the topic "Fractional calculus"

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Agarwal, Praveen, Dumitru Baleanu, YangQuan Chen, Shaher Momani, and José António Tenreiro Machado, eds. Fractional Calculus. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0430-3.

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Xue, Dingyü, and Lu Bai. Fractional Calculus. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-2070-9.

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C, McBride A., and Roach G. F, eds. Fractional calculus. Pitman Advanced Pub. Program, 1985.

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Anastassiou, George A. Generalized Fractional Calculus. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56962-4.

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Das, Shantanu. Functional Fractional Calculus. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20545-3.

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Goodrich, Christopher, and Allan C. Peterson. Discrete Fractional Calculus. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25562-0.

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Lorenzo, Carl F. Initialized fractional calculus. National Aeronautics and Space Administration, Glenn Research Center, 2000.

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Das, Shantanu. Functional Fractional Calculus. Springer-Verlag Berlin Heidelberg, 2011.

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Daftardar-Gejji, Varsha, ed. Fractional Calculus and Fractional Differential Equations. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9227-6.

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Rubin, Boris. Fractional integrals and potentials. Longman, 1996.

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Book chapters on the topic "Fractional calculus"

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Malinowska, Agnieszka B., Tatiana Odzijewicz, and Delfim F. M. Torres. "Fractional Calculus." In Advanced Methods in the Fractional Calculus of Variations. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14756-7_2.

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Mathai, A. M., Ram Kishore Saxena, and Hans J. Haubold. "Fractional Calculus." In The H-Function. Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0916-9_3.

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Petráš, Ivo. "Fractional Calculus." In Fractional-Order Nonlinear Systems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18101-6_2.

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Vyawahare, Vishwesh, and Paluri S. V. Nataraj. "Fractional Calculus." In Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7587-2_1.

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Gorenflo, R., and F. Mainardi. "Fractional Calculus." In Fractals and Fractional Calculus in Continuum Mechanics. Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-2664-6_5.

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Gorenflo, R. "Fractional Calculus." In Fractals and Fractional Calculus in Continuum Mechanics. Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-2664-6_6.

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Mainardi, F. "Fractional Calculus." In Fractals and Fractional Calculus in Continuum Mechanics. Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-2664-6_7.

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Lepik, Ülo, and Helle Hein. "Fractional Calculus." In Mathematical Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04295-4_8.

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Balachandran, K. "Fractional Calculus." In Industrial and Applied Mathematics. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-6080-4_2.

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de Oliveira, Edmundo Capelas, and José Emílio Maiorino. "Fractional Calculus." In Problem Books in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-74794-6_10.

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Conference papers on the topic "Fractional calculus"

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Oudetallah, Jamal, Imane Zouak, Wasim Audeh, et al. "Synchronization of Computer Virus System Using Fractional Calculus." In 2025 1st International Conference on Computational Intelligence Approaches and Applications (ICCIAA). IEEE, 2025. https://doi.org/10.1109/icciaa65327.2025.11013551.

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Alahmad, Rami, and Ahmad Abdelhadi. "Introduction to Fractional Calculus." In 2019 Advances in Science and Engineering Technology International Conferences (ASET). IEEE, 2019. http://dx.doi.org/10.1109/icaset.2019.8714417.

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"Applied fractional order calculus." In 2016 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR). IEEE, 2016. http://dx.doi.org/10.1109/aqtr.2016.7501362.

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Cruz-Duarte, Jorge M., and Porfirio Toledo-Hernández. "Fractional Calculus in Mexico: The 5th Mexican Workshop on Fractional Calculus (MWFC)." In MWFC 2022. MDPI, 2023. http://dx.doi.org/10.3390/cmsf2022004007.

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Zeng, Caibin, and YangQuan Chen. "Optimal Random Search, Fractional Dynamics and Fractional Calculus." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12734.

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What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Levy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In the paper we propose the Continuous Time Random Walk (C-TRW) optimal search framework and find the optimum for both of search length’s and waiting time’s distributions. Based on fractional calculus technique, we further derive its master equation to show the mechanism of such c
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Zhang, Yanshan, Feng Zhang, and Mingfeng Lu. "Relationship between fractional calculus and fractional Fourier transform." In SPIE Optical Engineering + Applications, edited by Oliver E. Drummond and Richard D. Teichgraeber. SPIE, 2015. http://dx.doi.org/10.1117/12.2187649.

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Schirmer, Pascal A., and Iosif Mporas. "Energy Disaggregation Using Fractional Calculus." In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2020. http://dx.doi.org/10.1109/icassp40776.2020.9054713.

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Liu, Kai, Xi Zhang, and YangQuan Chen. "Energy Informatics and Fractional Calculus." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67485.

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Energy informatics (EI) is relatively a blossoming and dynamic research area especially in today’s green manufacturing world. Using renewable energy and clean technology are the keys to a revitalization of the world manufacturing and job creation. Green manufacturing, which reduces resource use, waste and emissions and saving the energy, has become the priority for the manufacturers. Therefore, EI has come into a desirable solution. The fractional calculus (FC) is a mighty tool which can characterize the complex properties of the natural and social phenomena. In this paper, we have provided an
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Yangquan Chen. "Applied Fractional Calculus in controls." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5159794.

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Ma, Qingxia, Xianguang Lin, and Huijuan Li. "A Comparative Teaching of Fractional Calculus and Integer Calculus." In 2018 International Conference on Social Science and Education Reform (ICSSER 2018). Atlantis Press, 2018. http://dx.doi.org/10.2991/icsser-18.2018.22.

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Reports on the topic "Fractional calculus"

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D'Elia, Marta, Mamikon Gulian, George Karniadakis, and Hayley Olson. A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus. Office of Scientific and Technical Information (OSTI), 2020. http://dx.doi.org/10.2172/1618398.

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Altınkaya, Şahsene, Shigeyoshi Owa, and Sibel Yalçın. On a New Class of Analytic Functions Related to Fractional Calculus. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2020. http://dx.doi.org/10.7546/crabs.2020.01.02.

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D'Elia, Marta, Mamikon Gulian, Tadele Mengesha, and James Scott. Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1855046.

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