Existence of solution for fractional Langevin equation: Variational approach
نویسندگان
چکیده
منابع مشابه
Fractional Langevin equation.
We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffu...
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We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, wh...
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In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.
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In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.
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It is well known that the concept of diffusion is associated with random motion of particles in space, usually denoted as Brownian motion, see e.g. [1-3]. Diffusion is considered normal when the mean squared displacement of the particle during a time interval becomes, for sufficiently long intervals, a linear function of it. When this linearity breaks down, degenerating in a power law with expo...
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2014
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2014.1.54