Experimental evidence for fractional time evolution in glass forming materials

By Rudolf Hilfer. 2002

303 citations recorded by the source corpus.

Subfields: Ceramics and Composites, Materials Chemistry, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ed3ed2c098891d04fc51200f95a3200a081d3f76

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In Ceramics and Composites

In Materials Chemistry

In Modeling and Simulation

Citations in the corpus

Threefold Introduction to Fractional Derivatives (2008, background): “4] In recent times, however, fractional differential equations appear as “generalizations” of more or less fundamental equations of physics [3, 12, 18, 23, 43, 46, 52, 54–56, 58, 60, 90, 91, 102, 104, 119, 129].”
NONLOCAL PROBLEM FOR A MIXED TYPE FOURTH-ORDER DIFFERENTIAL EQUATION WITH HILFER FRACTIONAL OPERATOR (2020, methodology): “We also note [10, 11], where the generalized Riemann–Liouville operator was used in studying dielectric relaxation in glass-forming liquids with different chemical compositions.”
Existence and uniqueness for a problem involving Hilfer fractional derivative (2012, result): “Indeed, some of these models are supported by experimental evidence and yield results that agree with the observed behavior [19].”
Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives (2013, methodology): “We consider the so-called composite fractional relaxation equation (see [5])”
OPERATIONAL METHOD FOR THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES (2009, background): “Later GRLFD’s appeared also in the theoretical modeling of broadband dielectric relaxation spectroscopy for glasses [20].”
Existence of solutions for nonlinear fractional stochastic differential equations (2013, background): “Hilfer [6,7] showed that time fractional derivatives are equivalent to infinitesimal generators of generalized time fractional evolutions that arise in the transition from microscopic to macroscopic time scales.”
Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions (2010, background): “Hilfer [7] observed that a particular case of the fractional differential equation (3.”
Models of dielectric relaxation based on completely monotone functions (2016, background): “[8] S. Candelaresi, R. Hilfer, Excess wings in broadband dielectric spectroscopy.”
Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator (2012, background): “More recently, in [1,7,8] an infinite family of fractional (R–L) derivatives having the same order were introduced as follows.”
Heterogeneous dynamics in liquids: fluctuations in space and time (2002, background): “A particular case studied by Hilfer [62,63] replicates the Cole–Cole function, which corresponds to a symmetric loss peak on the log(ω) scale.”
FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS (2004, background): “fractals [27], glasses [28, 29], porous [30], and random [31] media.”
A practical guide to Prabhakar fractional calculus (2020, unknown): “[68, 69,111–113,147,150,155]).”