publication . Preprint . Article . 2016

Fractional Euler Limits and their Applications

Shev MacNamara; Bruce Henry; William McLean;
Open Access English
  • Published: 10 Sep 2016
Abstract
Generalizations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.
Subjects
arXiv: Mathematics::ProbabilityMathematics::Classical Analysis and ODEs
free text keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Probability, Applied mathematics, Mathematical analysis, Generalization, Fractional calculus, Master equation, Mathematics, Euler's formula, symbols.namesake, symbols
60 references, page 1 of 4

[1] L. Abadias and P. J. Miana, A subordination principle on wright functions and regularized resolvent families, Journal of Function Spaces, (2015).

[2] L. Altenberg, Resolvent positive linear operators exhibit the reduction phenomenon, Proceedings of the National Academy of Sciences, 109 (2012), pp. 3705{3710, doi:10.1073/pnas.1113833109. [OpenAIRE]

[3] C. N. Angstmann, I. C. Donnelly, and B. I. Henry, Pattern formation on networks with reactions: A continuous-time random-walk approach, Physical Review E, (2013).

[4] C. N. Angstmann, I. C. Donnelly, B. I. Henry, T. A. M. Langlands, and P. Straka, Generalized continuous time random walks, master equations, and fractional fokker{planck equations, SIAM Journal on Applied Mathematics, 75 (2015), pp. 1445{1468. [OpenAIRE]

[5] W. Arendt, C. Batty, M. Hieber, and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Birkhauser, 2011.

[6] B. Baeumer and M. M. Meerschaert, Stochastic solutions for fractional cauchy problems, Fractional Calculus and Applied Analysis, (2001).

[7] E. G. Bajlekova, Fractional Evolution Equations in Banach Spaces, PhD thesis, Technische Universiteit Eindhoven, 2001.

[8] B. P. Belinskiy and T. J. Kozubowski, Exponential mixture representation of geometric stable densities, Journal of Mathematical Analysis and Applications, 246 (2000), pp. 465{ 479. [OpenAIRE]

[9] Y. Berkowitz, Y. Edery, H. Scher, and B. Berkowitz, Fickian and non-Fickian di usion with bimolecular reactions, Phys. Rev. E, 87 (2013). [OpenAIRE]

[10] A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences, vol. 9, Society for Industrial and Applied Mathematics, Philadelphia, 1994. [OpenAIRE]

[11] E. Blanc, S. Engblom, A. Hellander, and P. Lotstedt, Mesoscopic modeling of stochastic reaction-di usion kinetics in the subdi usive regime, Multiscale Modeling & Simulation, 14 (2016), pp. 668{707, doi:10.1137/15M1013110.

[12] S. Bochner, Harmonic Analysis and the Theory of Probability, Dover, 2005.

[13] K. Burrage and G. Lythe, Accurate stationary densities with partitioned numerical methods for stochastic di erential equations, SIAM Journal on Numerical Analysis, 47 (2009), pp. 1601{1618. [OpenAIRE]

[14] A. V. Chechkin, R. Gorenflo, and I. M. Sokolov, Fractional di usion in inhomogeneous media, Journal of Physics A: Mathematical and General, 38 (2005), p. L679. [OpenAIRE]

[15] B. Drawert, M. Trogdon, S. Toor, L. Petzold, and A. Hellander, Molns: A cloud platform for interactive, reproducible, and scalable spatial stochastic computational experiments in systems biology using pyurdme, SIAM Journal on Scienti c Computing, 38 (2016), pp. C179{C202, doi:10.1137/15M1014784. [OpenAIRE]

60 references, page 1 of 4
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