Experimental evidence for fractional time evolution in glass forming materials

Hilfer, R.

doi:10.1016/s0301-0104(02)00670-5

Cited by 293 publications

(221 citation statements)

References 25 publications

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“…For the example of broadband dielectric spectroscopy in glasses, generalized relaxation functions and susceptibilities based on Equation (70) have already been successfully compared to experiments [23,[29][30][31][32]. Theoretical, mathematical and experimental studies are encouraged to further explore the consequences of the generalized concept.…”

Section: Discussionmentioning

confidence: 99%

Time Automorphisms on C*-Algebras

Hilfer

2015

Mathematics

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Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C * -algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.

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Section: Discussionmentioning

confidence: 99%

Time Automorphisms on C*-Algebras

Hilfer

2015

Mathematics

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“…The case with δ = 0 corresponds to the so-called Hilfer composite fractional derivative of order 0 < µ < 1 and type 0 ≤ν ≤ 1, which is given [24]. This composite fractional derivative has been successfully applied in description of dielectric and viscoelastic phenomena [25,26].…”

Section: Prabhakar Derivativesmentioning

confidence: 99%

“…Here we note that different fractional equations have been used for modeling anomalous diffusion in various systems, including fractional reaction-diffusion equations [27,28] and their application [29], fractional relaxation and diffusion equations [5,6,9,10,[24][25][26], fractional cable equation [30], etc.…”

Section: Prabhakar Derivativesmentioning

confidence: 99%

Generalized Langevin Equation and the Prabhakar Derivative

Sandev

2017

Mathematics

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“…Beside Caputo and Riemann-Liouville fractional derivatives, there exists a new definition of fractional derivative introduced by Hilfer, which generalized the concept of Riemann-Liouville derivative and has many application in physics, for more details, see [10][11][12]25].…”

Section: Introductionmentioning

confidence: 99%

Null controllability of nonlocal Hilfer fractional stochastic differential equations

JinRong¹,

Ahmed²

2017

MMN

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Abstract. In this paper, we study exact null controllability of Hilfer fractional semilinear stochastic differential equations in Hilbert spaces. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional systems are established. An example is given to show the application of our results.2010 Mathematics Subject Classification: 26A33; 93B05

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Experimental evidence for fractional time evolution in glass forming materials

Cited by 293 publications

References 25 publications

Time Automorphisms on C*-Algebras

Time Automorphisms on C*-Algebras

Generalized Langevin Equation and the Prabhakar Derivative

Null controllability of nonlocal Hilfer fractional stochastic differential equations

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