FRACTIONAL TIME EVOLUTION

By Rudolf Hilfer. 2000

308 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d32352233cc2f6e718cad81381397b8debe259b4

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In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Discrete random walk models for space-time fractional diffusion (2002, unknown): “[1], [10], [15], [28] [29, 30], [34, 35, 36], [40], [48, 49], [52], [57], [61, 62], [63, 64].”
Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative (2013, methodology): “In introducing this new fractional derivative we were motivated by the Hilfer fractional derivative of order 0 < α < 1 and type 0 ≤ β ≤ 1 (see [7])”
OPERATIONAL METHOD FOR THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES (2009, background): “For n = 1 this solution was first given in [17].”
Experimental evidence for fractional time evolution in glass forming materials (2002, background): “3] In [6](see also [7, 3] for later references) specific examples of [page 400, §0] fractional time evolution, namely fractional diffusion and master equations, were for the first time identified as special cases of the well developed theory of continuous time random walks [8, 9, 10, 11, 12, 13, 14,”
Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel (2009, background): “We remark in passing that Hilfer (see [8,9]) generalized the Riemann–Liouville fractional derivative operator Daþ in (1.”
Fox H functions in fractional diffusion (2005, unknown): “[1,11–13,15,26–29,32–36].”
Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions (2010, background): “These equations are investigated in order to determine and interpret certain physical phenomena which govern such processes as diffusion in porous media, reaction and relaxation in complex systems, anomalous diffusion, and so on [5,6].”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “These equations are investigated in order to determine and interpret certain physical phenomena which govern such processes as diffusion in porous media, reaction and relaxation in complex systems, anomalous diffusion, and so on (see also [28, 36]).”