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Relevant bibliographies by topics / Mittag-leffler

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Academic literature on the topic 'Mittag-leffler'

Author: Grafiati

Published: 4 June 2021

Last updated: 23 February 2023

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Journal articles on the topic "Mittag-leffler"

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Paneva-Konovska, Jordanka. "Differential and integral relations in the class of multi-index Mittag-Leffler functions." Fractional Calculus and Applied Analysis 21, no. 1 (2018): 254–65. http://dx.doi.org/10.1515/fca-2018-0016.

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Abstract As recently observed by Bazhlekova and Dimovski [1], the n-th derivative of the 2-parametric Mittag-Leffler function gives a 3-parametric Mittag-Leffler function, known as the Prabhakar function. Following this analogy, the n-th derivative of the (2m-index) multi-index Mittag-Leffler functions [6] is obtained, and it turns out that it is expressed in terms of the (3m-index) Mittag-Leffler functions [10, 11]. Further, some special cases of the fractional order Riemann-Liouville and Erdélyi-Kober integrals of the Mittag-Leffler functions are calculated and interesting relations are prov

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Zhang, Yanyan, Ghulam Farid, Zabidin Salleh, and Ayyaz Ahmad. "On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator." Mathematical Problems in Engineering 2021 (October 13, 2021): 1–9. http://dx.doi.org/10.1155/2021/6043769.

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The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fra

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Haubold, H. J., A. M. Mathai, and R. K. Saxena. "Mittag-Leffler Functions and Their Applications." Journal of Applied Mathematics 2011 (2011): 1–51. http://dx.doi.org/10.1155/2011/298628.

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Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions, and their interesting and useful properties. Applications of G. M. Mittag-Leffler functions in certain areas of physical and applied sciences are also demonstrated. During the last two decades this function has come into prominence after about nine decades of its discovery by a Swe

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Hanneken, John W., and B. N. Narahari Achar. "Finite Series Representation of the Inverse Mittag-Leffler Function." Mathematical Problems in Engineering 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/252393.

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The inverse Mittag-Leffler functionEα,β-1zis valuable in determining the value of the argument of a Mittag-Leffler function given the value of the function and it is not an easy problem. A finite series representation of the inverse Mittag-Leffler function has been found for a range of the parametersαandβ; specifically,0<α<1/2forβ=1and forβ=2. This finite series representation of the inverse Mittag-Leffler function greatly expedites its evaluation and has been illustrated with a number of examples. This represents a significant advancement in the understanding of Mittag-Leffler functions

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Rothmaler, Philipp. "Mittag-Leffler modules." Annals of Pure and Applied Logic 88, no. 2-3 (1997): 227–39. http://dx.doi.org/10.1016/s0168-0072(97)00024-9.

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Jayakumar, K. "Mittag-leffler process." Mathematical and Computer Modelling 37, no. 12-13 (2003): 1427–34. http://dx.doi.org/10.1016/s0895-7177(03)90050-1.

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Paneva-Konovska, Jordanka. "Taylor Series for the Mittag–Leffler Functions and Their Multi-Index Analogues." Mathematics 10, no. 22 (2022): 4305. http://dx.doi.org/10.3390/math10224305.

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It has been obtained that the n-th derivative of the 2-parametric Mittag–Leffler function is a 3-parametric Mittag–Leffler function, with exactness to a constant. Following the analogy, the author later obtained the n-th derivative of the 2m-parametric multi-index Mittag–Leffler function. It turns out that this is expressed via the 3m-parametric Mittag–Leffler function. In this paper, upper estimates of the remainder terms of these derivatives are found, depending on n. Some asymptotics are also found for “large” values of the parameters. Further, the Taylor series of the 2 and 2m-parametric M

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Srivastava, Hari M., Arran Fernandez, and Dumitru Baleanu. "Some New Fractional-Calculus Connections between Mittag–Leffler Functions." Mathematics 7, no. 6 (2019): 485. http://dx.doi.org/10.3390/math7060485.

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We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential a

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Apelblat, Alexander. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach." Mathematics 8, no. 5 (2020): 657. http://dx.doi.org/10.3390/math8050657.

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In this work, properties of one- or two-parameter Mittag-Leffler functions are derived using the Laplace transform approach. It is demonstrated that manipulations with the pair direct–inverse transform makes it far more easy than previous methods to derive known and new properties of the Mittag-Leffler functions. Moreover, it is shown that sums of infinite series of the Mittag-Leffler functions can be expressed as convolution integrals, while the derivatives of the Mittag-Leffler functions with respect to their parameters are expressible as double convolution integrals. The derivatives can als

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Kumar, Dinesh, Jeta Ram, and Junesang Choi. "Dirichlet Averages of Generalized Mittag-Leffler Type Function." Fractal and Fractional 6, no. 6 (2022): 297. http://dx.doi.org/10.3390/fractalfract6060297.

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Since Gösta Magus Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903 and studied its features in five subsequent notes, passing the first half of the 20th century during which the majority of scientists remained almost unaware of the function, the Mittag-Leffler function and its various extensions (referred to as Mittag-Leffler type functions) have been researched and applied to a wide range of problems in physics, biology, chemistry, and engineering. In the context of fractional calculus, Mittag-Leffler type functions have been widely studied. Since Carlson established th

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Dissertations / Theses on the topic "Mittag-leffler"

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Bersani, Marco. "Sul teorema di Mittag-Leffler." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/796/.

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Rosendo, Danilo Castro. "Sobre a função de Mittag-Leffler." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307007.

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Orientador: Edmundo Capelas de Oliveira<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-11T17:01:55Z (GMT). No. of bitstreams: 1 Rosendo_DaniloCastro_M.pdf: 1231397 bytes, checksum: 33e1a80ea06fa615b7b7aec7917bbbe2 (MD5) Previous issue date: 2008<br>Resumo: Neste trabalho abordamos um estudo da equação diferencial ordinária, linear, homogênea de segunda ordem com três singularidades regulares, incluindo uma no infinito de onde obtivemos a equação hipergeométrica e,

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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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Contharteze, Eliana 1984. "Equações diferenciais fracionárias e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306993.

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Orientador: Edmundo Capelas de Oliveira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:22:44Z (GMT). No. of bitstreams: 1 Contharteze_Eliana_D.pdf: 2292843 bytes, checksum: c606ccefade98acff6e3f2b74c2ac021 (MD5) Previous issue date: 2014<br>Resumo: Apresentamos operadores de integração e derivação fracionárias, que em particular, podem ser utilizados para descrever um processo difusivo anômalo através de uma equação diferencial fracionária. Como aplicação, discutimos uma equaçã

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Moschen, Izolda Del Corno. "Sobre as funções Mittag-Leffler e o modelo fracionário de materiais viscoelásticos." Florianópolis, SC, 2006. http://repositorio.ufsc.br/xmlui/handle/123456789/88441.

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Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Mecânica.<br>Made available in DSpace on 2012-10-22T09:04:38Z (GMT). No. of bitstreams: 1 241191.pdf: 1032630 bytes, checksum: 7eb9b1567a932ceb82a61ee88e2ac63a (MD5)<br>Materiais viscoelásticos são hoje largamente aplicados em vários ramos da engenharia, com destaque para a mecânica e aeroespacial. Uma das razões para tal popularidade reside na facilidade com que os materiais viscoelásticos são vulcanizados nas mais diferentes formas. Outra, é o fato de que inúmeros materiais básicos pod

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Jahnert, Florian [Verfasser], and Martin [Akademischer Betreuer] Grothaus. "Construction of a Mittag-Leffler Analysis and its Applications / Florian Jahnert. Betreuer: Martin Grothaus." Kaiserslautern : Technische Universität Kaiserslautern, 2015. http://d-nb.info/1075756987/34.

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Barelli, Eleonora. "Dielectric relaxation in biological materials." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9102/.

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The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important in order to explain various phenomena in Solid-State Physics and in Physics of Biological Materials. Indeed, during the last two centuries, many scientists have tried to explain and model the dielectric relaxation. Starting from the Kohlrausch model and passing through the ideal Debye one, they arrived at more com- plex models that try to explain the experimentally observed distributions of relaxation times, including the classical (Cole-Cole, Davidson-Co

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Camargo, Rubens de Figueiredo. "Calculo fracionario e aplicações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307012.

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Orientadores: Edmundo Capelas de Oliveira, Ary Orozimbo Chiacchio<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T21:42:46Z (GMT). No. of bitstreams: 1 Camargo_RubensdeFigueiredo_D.pdf: 9956358 bytes, checksum: 45d7b7d76ae44d9b713d341ffc7a1ad5 (MD5) Previous issue date: 2009<br>Resumo: Apresentamos neste trabalho um estudo sistemático e detalhado sobre integrais e derivadas de ordens arbitrárias, o assim chamado cálculo de ordem não-inteira, popularizado com o nome de Cálculo Fraci

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Neto, Paulo Mendes de Carvalho. "Fractional differential equations: a novel study of local and global solutions in Banach spaces." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06062013-145531/.

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Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study several matters related to abstract fractional Cauchy problems of order \'alpha\' \'it belongs\' (0, 1). We search to answer some questions that were open: for instance, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally,

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Books on the topic "Mittag-leffler"

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Stubhaug, Arild. Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8.

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Kochina, P. I︠A︡. Gësta Mittag-leffler, 1846-1927. "Nauka", 1987.

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Gësta Mittag-Leffler, 1846-1927. "Nauka", 1987.

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

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Gorenflo, Rudolf, Anatoly A. Kilbas, Francesco Mainardi, and Sergei V. Rogosin. Mittag-Leffler Functions, Related Topics and Applications. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43930-2.

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Gorenflo, Rudolf, Anatoly A. Kilbas, Francesco Mainardi, and Sergei Rogosin. Mittag-Leffler Functions, Related Topics and Applications. Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-61550-8.

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Poincaré, Henri. La correspondance entre Henri Poincaré et Gösta Mittag-Leffler. Birkhäuser, 1999.

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Kilbas, Anatoly A., Sergei V. Rogosin, Francesco Mainardi, and Rudolf Gorenflo. Mittag-Leffler Functions, Related Topics and Applications. Springer, 2014.

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Gösta Mittag-Leffler: A Man of Conviction. Springer, 2010.

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Stubhaug, Arild, and Tiina Nunnally. Gösta Mittag-Leffler: A Man of Conviction. Springer, 2016.

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Book chapters on the topic "Mittag-leffler"

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Capelas de Oliveira, Edmundo. "Mittag-Leffler Functions." In Studies in Systems, Decision and Control. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20524-9_3.

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Agarwal, Ravi P., Kanishka Perera, and Sandra Pinelas. "Mittag-Leffler Theorem." In An Introduction to Complex Analysis. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4614-0195-7_44.

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Stubhaug, Arild. "Leffler and Mittag." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_3.

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Diethelm, Kai. "Mittag-Leffler Functions." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14574-2_4.

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Stubhaug, Arild. "Journey at the Turn of the Century." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_1.

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Stubhaug, Arild. "The Aristocracy of Lennartsnäs." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_10.

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Stubhaug, Arild. "Controversy over the Academic Degree Regulations." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_11.

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Stubhaug, Arild. "His Sister’s Debut and His Father’s Illness." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_12.

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Stubhaug, Arild. "First Trip Abroad." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_13.

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Stubhaug, Arild. "The Stablemaster at Övrejärva." In Gösta Mittag-Leffler. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11672-8_14.

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Conference papers on the topic "Mittag-leffler"

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Niu, Haoyu, Yuquan Chen, and YangQuan Chen. "Fractional-Order Extreme Learning Machine With Mittag-Leffler Distribution." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97652.

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Abstract Extreme Learning Machine (ELM) has a powerful capability to approximate the regression and classification problems for a lot of data. ELM does not need to learn parameters in hidden neurons, which enables ELM to learn a thousand times faster than conventional popular learning algorithms. Since the parameters in the hidden layers are randomly generated, what is the optimal randomness? Lévy distribution, a heavy-tailed distribution, has been shown to be the optimal randomness in an unknown environment for finding some targets. Thus, Lévy distribution is used to generate the parameters i

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Hanneken, John W., David M. Vaught, and B. N. Narahari Achar. "The Number of Real Zeros of the Single Parameter Mittag-Leffler Function for Parameter Values Between 1 and 2." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84172.

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The single parameter Mittag-Leffler function, which is a generalization of the exponential function, occurs naturally in the solution of physical problems involving fractional calculus and its zeros play a significant role in the dynamic solutions. It is known that the Mittag-Leffler function has a finite number of real zeros in the range of parameter values between 1 and 2, which is quite relevant for many physical problems. However, the number of real zeros for a given parameter value in this range is not known. An iteration formula for calculating the number of real zeros of the Mittag-Leff

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MAINARDI, FRANCESCO, RUDOLF GORENFLO, and ENRICO SCALAS. "A RENEWAL PROCESS OF MITTAG-LEFFLER TYPE." In Fractals and Related Phenomena in Nature. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702746_0002.

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Wei, Jiamin, YangQuan Chen, Yongguang Yu, and Yuquan Chen. "Improving Cuckoo Search Algorithm With Mittag-Leffler Distribution." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97709.

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Abstract Cuckoo search (CS), as one of the recent nature-inspired metaheuristic algorithms, has proved to be an efficient approach due to the combination of Lévy flights, local search capabilities and guaranteed global convergence. CS uses Lévy flights in global random walk to explore the search space. The Lévy step is taken from the Lévy distribution which is a heavy-tailed probability distribution. In this case, a fraction of large steps are generated, which plays an important role in enhancing search capability of CS. Besides, although many foragers and wandering animals have been shown to

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Paneva-Konovska, J., Michail D. Todorov, and Christo I. Christov. "Convergence of Series in Mittag-Leffler Type Functions." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: Proceedings of the 2nd International Conference. AIP, 2010. http://dx.doi.org/10.1063/1.3526665.

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Podlubny, Igor, Ivo Petras, and Tomas Skovranek. "Fitting of experimental data using Mittag-Leffler function." In 2012 13th International Carpathian Control Conference (ICCC). IEEE, 2012. http://dx.doi.org/10.1109/carpathiancc.2012.6228711.

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Teodoro, Graziane Sales, and Edmundo Capelas de Oliveira. "Funções de Mittag-Leffler e a transformada de laplace." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0208.

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Paneva-Konovska, Jordanka. "Fatou type theorems for series in Mittag-Leffler functions." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766800.

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KILBAS, A. A., and A. A. KOROLEVA. "INTEGRAL TRANSFORM WITH THE EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0018.

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Luo, LaiHui, and YongBing Hu. "Global Mittag-Leffler Synchronization Fractional Complex Value Neural Networks." In 2022 IEEE 5th International Conference on Electronic Information and Communication Technology (ICEICT). IEEE, 2022. http://dx.doi.org/10.1109/iceict55736.2022.9909196.

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Reports on the topic "Mittag-leffler"

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Raza, Mohsan, and Muhey U. Din. Close-to-convexity of q‑Mittag‑Leffler Functions. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2018. http://dx.doi.org/10.7546/crabs.2018.12.01.

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Cetinkaya, Asena. Multivalent Functions Involving Srivastava–Tomovski Generalization of the Mittag-Leffler Function Defined in the Nephroid Domain. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2021. http://dx.doi.org/10.7546/crabs.2021.02.02.

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