Hamiltonian Chaos and Fractional Dynamics

By M. Combescure. 2005

814 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0d46a394e3efacfdd39a3d9485191a6dbab6c0c6

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In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

LYAPUNOV-KRASOVSKII STABILITY THEOREM FOR FRACTIONAL SYSTEMS WITH DELAY (2011, background): “During the last years fractional calculus was subjected to an intense debate [1-4].”
Time-fractional Diffusion of Distributed Order (2007, methodology): “For further reading on the theory and applications of fractional calculus we recommend to consult in addition to the well-known books by Samko, Kilbas & Marichev [49], by Miller & Ross [45], by Podlubny [47], those appeared in the last few years, by Kilbas, Srivastava & Trujillo [28], by Magin [32],”
Fractional order models of leaves (2014, methodology): “During the last decade FC has been found to play a fundamental role in the modeling of a considerable number of phenomena (Oustaloup, 1991; Zaslavsky, 2005; Magin, 2006; Mainardi, 2010; Monje et al., 2010; Tenreiro Machado et al., 2011a), and has emerged as an important tool for the study of…”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, neutral): “Introduction Fractional calculus theory [1–3] has been applied to a wide class of complex problems encompassing physics, biology, mechanics, and interdisciplinary areas [4–9].”
Time-fractional derivatives in relaxation processes: a tutorial survey (2008, background): “our CISM Lecture Notes [55, 57, 80], the review papers [85, 86, 116], and the books [88, 70, 66, 69, 77, 94, 108, 118, 119] with references therein.”
The Chronicles of Fractional Calculus (2017, neutral): “1980-1989 [183, 184, 146, 136, 162, 176, 137, 138] [125] 1990 [186] [68] 1991 [140, 139, 147, 61] 1992 [182, 33, 177, 130] [80] 1993 1994 [206, 85] 1995 [148] [172] 1996 [141, 170] 1997 [34, 118] 1998 [128] [173, 123] 1999 [158, 150, 193, 199] 2000 [67] 2001 [9, 13] [16] 2002 [201, 157, 54, 73, 72] ”
Fractional hamilton formalism within caputo’s derivative (2006, background): “A huge amount of mathematical knowledge on fractional integrals and derivatives has been constructed [1-8].”
Continuous-time random walk and parametric subordination in fractional diffusion (2007, neutral): “The reader interested to these processes is referred to several educational/review papers and books, including [35,36,42,49,55,59,61,63,64].”
The Geometric Foundations of Hamiltonian Monte Carlo (2014, background): “The Hamiltonian flow generated from a single point may explore the entirety of the corresponding level set or be restricted to a smaller submanifold of the level set, but in either case the trajectory nearly closes in some possibly-long but finite recurrence time, τH−1(E) [56,78].”
Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative (2014, background): “[5–11] and references therein), they attract considerable interest and there has been a significant theoretical development recently (for example, see Refs.”