1,470 research outputs found
Sobre as funções Mittag-Leffler e o modelo fracionário de materiais viscoelásticos
No full textTese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Mecânica.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 podem ter suas propriedades dinâmicas adequadas, mediante introdução de aditivos, às várias aplicações específicas. O Grupo PISA-LVA os vem estudando, bem como suas aplicações, há cerca de quinze anos, tendo já granjeado reputação internacional. Dentre as suas conquistas, cite-se, por importante no presente trabalho, o desenvolvimento de técnica para a identificação dos parâmetros do modelo fracionário dos materiais viscoelásticos. Esta técnica, já difundida internacionalmente, acabou por substituir, no âmbito do Grupo, com enormes vantagens, a da norma ASTM E 756 98. Esta técnica é toda estabelecida no domínio da freqüência. Surge naturalmente a questão: se esses parâmetros representam o material viscoelástico com excelente precisão, não seria correto utilizá-los para o cômputo de propriedades importantes, definidas no domínio do tempo, como creep, compression set e outras? Este trabalho pretende ser um passo inicial para responder a essas questões, entre outras. Revê os modelos de Maxell, Kelvin-Voigt e Linear Padrão (ou Zener), primeiro na forma clássica, a derivadas inteiras. Repete-se este estudo, agora permitindo que as derivadas tenham ordem fracionária. As equações resultantes são tratadas pela via da Transformada de Laplace. As soluções das equações resultantes envolvem as funções de Mittag-Leffler, notórias pelas dificuldades computacionais que apresentam, em certas circunstâncias. Embora inúmeros estudos e algoritmos tenham vindo recentemente à luz, parece, entretanto, que um algoritmo absolutamente robusto, infenso a toda e qualquer circunstância, ainda está para ser escrito. Como a função de creep é bem comportada para o computo numérico, procura-se calcular a função de relaxação de tensão por deconvolução. Uma outra saída, também aqui apresentada, é a da inversão numérica da transformada de Laplace. Os resultados dessas técnicas são cotejados com aqueles obtidos pelo cômputo direto da função de Mittag-Leffler, em casos em que há convergência
Boundedness of fractional integral operators containing mittag-leffler functions via (S, m)-convexity
No full textThe objective of this paper is to derive the bounds of fractional integral operators which contain Mittag-Leffler functions in the kernels. By using (s, m)-convex functions bounds of these operators are evaluated which lead to obtain their boundedness and continuity. Moreover the presented results can be used to get various results for known fractional integrals and functions deducible from (s, m)-convexity. Also a version of Hadamard type inequality is established for (s, m)-convex functions via generalized fractional integrals. © 2020 the Author(s)
Generalized Mittag-Leffler kernels and generalized scaling operators in Mittag-Leffler analysis
No full textGeneralized scaling operators and generalized Gauss kernels are fundamental concepts in Gaussian analysis with application to path integrals and PDEs via the Feynman-Kac formula. In non-Gaussian analysis, particularly in Mittag-Leffler analysis, i.e., in the case when compared to a Gaussian characteristic function the exponential is replaced by a Mittag-Leffler function, these concepts are unknown. In view of this, we elaborate in this article the generalized scaling and generalized Mittag-Leffler kernels and prove a form of a Wick-type product formula. We give some first examples for generalized scaling.Узагальнені оператори масштабування та узагальнені ядра Гаусса становляь фундаментальні поняття гаусового аналізу та мають застосування до інтегралів за шляхами та рівнянь у частинних похідних з використанням формули Фейнмана-Каца. Це є новим в негаусівського аналізу, зокрема в аналізі Міттага-Леффлера, тобто у випадку якщо в гаусовій характеристичній функції експонента замінюється функцією Міттага-Леффлера. З огляду на це, в статті детально розглянуто ядра узагальненого масштабування та узагальнені ядра Міттага-Леффлера, та доведено форма формулу добутку Віковського типу. Наведено кілька перших прикладів узагальненого масштабування
Properties on subclass of Sakaguchi type functions using a Mittag-Leffler type Poisson distribution series
No full textsummary:Few subclasses of Sakaguchi type functions are introduced in this article, based on the notion of Mittag-Leffler type Poisson distribution series. The class is defined, and the necessary and sufficient condition, convex combination, growth distortion bounds, and partial sums are discussed
Refinement and corrigendum of bounds of fractional integral operators containing mittag-leffler functions
No full textThe main objective of this paper is to compute refinements of bounds of the generalized fractional integral operators containing an extended generalized Mittag-Leffler function in their kernels. The presented results also provide refinements of already known bounds of different fractional integral operators for convex, m-convex, s-convex and (s, m)-convex functions. Moreover, the refinements of some known fractional versions of the Hadamard inequality are given. © 2020 the Author(s), licensee AIMS Press
Comments on the properties of Mittag-Leffler function
No full textThe properties of Mittag-Leffler function are reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schrödinger type and heat-type fractional partial differential equations and explore the problem of operatorial ordering finding appropriate rules when non-commuting operators are involved. We discuss the coherent states associated with the fractional Schödinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature. © 2018, EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
The New Mittag-Leffler Function and Its Applications
No full textIn this paper, we investigate some properties of the Pochhammer p,s,k-symbol ξn,k,sp and gamma p,s,k-function Γs,kpξ. We then prove several identities for newly defined symbol ξn,k,sp and the function Γs,kpξ. The integral representations for the gamma p,s,k-function and beta p,s,k-function are presented. Also, we define a new Mittag-Leffler p,s,k-function and study its analytic properties and its transforms
PERIPHERY BEHAVIOUR OF SERIES IN MITTAG-LEFFLER TYPE FUNCTIONS, II
No full textAbstract: This is a survey on a part of author's recent results on the subject. It is devoted to different systems of the Mittag-Leffler functions and their 3-parametric generalizations. First, asymptotic formulae necessary for obtaining the main results, are provided. Series defined by means of these systems are further studied. Starting with their domains of convergence, the behaviours of such series on the peripheries of their convergence domains are investigated and analogues of the classical results for the power series are proposed. This serves as Part II, of our previous pape
PERIPHERY BEHAVIOUR OF SERIES IN MITTAG-LEFFLER TYPE FUNCTIONS, I
No full textAbstract: This is a survey on part of author's recent results on the subject. Different families of the the Mittag-Leffler functions and their 3-parametric generalizations are considered. First, asymptotic formulae necessary for proving the main results, are provided. Series defined by means of these families are further studied. Starting with their domains of convergence, the behaviour of such series on the peripheries of their convergence domains is investigated and analogues of the classical results for the power series are proposed
A random telegraph signal of Mittag-Leffler type
No full textA general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations. Non-Poisson dichotomous noise is non-stationary and standard spectral methods fail to describe it properly as they assume stationarit
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