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Theorem for Series in Three-Parameter Mittag-Leffler Function
The new result presented here is a theorem involving series in the threeparameter Mittag-Le†er function. As a by-product, we recover some known results and discuss corollaries. As an application, weExpand
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On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag–Leffler noise. The solution ofExpand
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On some fractional Green’s functions
In this paper we discuss some fractional Green’s functions associated with the fractional differential equations which appear in several fields of science, more precisely, the so-called waveExpand
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Differentiation to fractional orders and the fractional telegraph equation
Using methods of differential and integral calculus, we present and discuss the calculation of a fractional Green function associated with the one-dimensional case of the so-called general fractionalExpand
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A prelude to the fractional calculus applied to tumor dynamic
In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation,Expand
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Solution of the fractional Langevin equation and the Mittag–Leffler functions
We introduce the fractional generalized Langevin equation in the absence of a deterministic field, with two deterministic conditions for a particle with unitary mass, i.e., an initial condition andExpand
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Analysis of fractional-order models for hepatitis B
This paper presents two models for hepatitis B, both given by fractional differential equations. The first model is formulated without parameters that indicate drug therapy, while the second oneExpand
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On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation
The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalizedExpand
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Integral representations of Mittag-Leffler function on the positive real axis
The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N.Expand
Stability analysis and numerical simulations via fractional calculus for tumor dormancy models
TLDR
We investigate two proposed ordinary differential equation systems via fractional calculus, which address dynamics between tumor cells and the immune system, and show two important behaviors associated with tumor dormancy. Expand
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