On Mittag-Leffler-type functions in fractional evolution processes
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TLDR
In this article, a variety of fractional evolution processes are reviewed, whose solutions turn out to be related to Mittag-Leffler-type functions, and the chosen equations are the simplest of the fractional calculus and include the Abel integral equations of the second kind.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2000-06-01 and is currently open access. It has received 540 citations till now. The article focuses on the topics: Fractional calculus & Integral equation.read more
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Fractional Calculus: Integral and Differential Equations of Fractional Order
TL;DR: In this article, the authors introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus, and derive the analytical solutions of the most simple linear integral and differential equations in fractional order.
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The fundamental solution of the space-time fractional diffusion equation
TL;DR: In this paper, the Cauchy problem for the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation.
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Mittag-Leffler Functions and Their Applications
TL;DR: In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented and an attempt is made to present nearly an exhaustive list of references to make the reader familiar with the present trend of research in Mittag, Leffler, and type functions and their applications.
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Mittag-Leffler Functions and Their Applications
TL;DR: A detailed survey of Mittag-Leffler type functions can be found in this article, where the authors present a detailed account or rather a brief survey of the Mittag Leffler function, generalized Mittag leffler functions and their interesting and useful properties.
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Fractional heat conduction equation and associated thermal stress
TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
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Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.