Title: APPLICATIONS OF FRACTIONAL CALCULUS TECHNIQUES TO PROBLEMS IN BIOPHYSICS
Abstract: Applications of Fractional Calculus in Physics, pp. 377-427 (2000) No AccessAPPLICATIONS OF FRACTIONAL CALCULUS TECHNIQUES TO PROBLEMS IN BIOPHYSICSTHEO F. NONNENMACHER and RALF METZLERTHEO F. NONNENMACHERDepartment of Mathematical Physics, University of Ulm, Albert–Einstein–Allee 11, 89069 Ulm/Donau, Germany and RALF METZLERDepartment of Mathematical Physics, University of Ulm, Albert–Einstein–Allee 11, 89069 Ulm/Donau, Germanyhttps://doi.org/10.1142/9789812817747_0008Cited by:16 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Fractional calculus Preliminary remarks Definition(s) of fractional differ–integrals Power–law relations and asymptotic fractals Some comments on the definitions Relaxation processes Memory integrals Markovian chains and Bernoulli scaling in ion channelling Some comments on fractional relaxation equations Fractional constitutive rheological models Application to filled polymers Results Equilibrium modulus Fractional protein dynamics Anomalous diffusion Fickean diffusion Cattaneo diffusion Properties of anomalous diffusion Fractional diffusion equations Spectral transforms Anomalous diffusion and fluorescence recovery Anomalous diffusion and NMR in biological tissue Generalised Cattaneo equations (GCEs) Conclusions Acknowledgements Appendix. Stable laws Appendix. Fox' H–functions Appendix. Fractal Fourier transform References FiguresReferencesRelatedDetailsCited By 16Time-fractional approach to the electrochemical impedance: The Displacement currentG. Barbero, L.R. Evangelista and E.K. Lenzi1 Sep 2022 | Journal of Electroanalytical Chemistry, Vol. 920Optimality conditions involving the Mittag–Leffler tempered fractional derivativeRicardo Almeida and M. Luísa Morgado1 Jan 2022 | Discrete & Continuous Dynamical Systems - S, Vol. 15, No. 3Fractional relaxation noises, motions and the fractional energy balance equationShaun Lovejoy25 February 2022 | Nonlinear Processes in Geophysics, Vol. 29, No. 1Delayed analogue of three‐parameter Mittag‐Leffler functions and their applications to Caputo‐type fractional time delay differential equationsIsmail T. Huseynov and Nazim I. Mahmudov28 July 2020 | Mathematical Methods in the Applied Sciences, Vol. 6417Fractional Calculus in BiomechanicsSergei Bosiakov25 January 2020Fractional Calculus in BiomechanicsSergei Bosiakov14 September 2018Viscoelasticity and pattern formations in stock market indicesGüngör Gündüz and Aydın Gündüz5 June 2017 | The European Physical Journal B, Vol. 90, No. 6How to identify absorption in a subdiffusive mediumT. Kosztołowicz, K.D. Lewandowska and T. Klinkosz30 December 2017 | Mathematical Modelling of Natural Phenomena, Vol. 12, No. 6Existence and approximation of solutions of fractional order iterative differential equationsJianHua Deng and JinRong Wang1 Jan 2013 | Open Physics, Vol. 11, No. 10Modern Rheology on a Stock Market: Fractional Dynamics of IndicesM. Kozłowska and R. Kutner1 Oct 2010 | Acta Physica Polonica A, Vol. 118, No. 4Rheological representation of fractional order viscoelastic material modelsKaterina D. Papoulia, Vassilis P. Panoskaltsis, Nishu V. Kurup and Igor Korovajchuk20 February 2010 | Rheologica Acta, Vol. 49, No. 4Singular Dynamics of Various Macroeconomic SectorsM. Kozłowska and R. Kutner1 Apr 2010 | Acta Physica Polonica A, Vol. 117, No. 4Fractional radial diffusion in an infinite medium with a cylindrical cavityY. Povstenko7 January 2009 | Quarterly of Applied Mathematics, Vol. 67, No. 1Time-fractional radial diffusion in a sphereYuriy Povstenko11 September 2007 | Nonlinear Dynamics, Vol. 53, No. 1-2Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanicsMingyu Xu and Wenchang Tan1 Jun 2006 | Science in China Series G, Vol. 49, No. 3Fractional Diffusion Based on Riemann-Liouville Fractional DerivativesR. Hilfer4 April 2000 | The Journal of Physical Chemistry B, Vol. 104, No. 16 Applications of Fractional Calculus in PhysicsMetrics History PDF download
Publication Year: 2000
Publication Date: 2000-03-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 27
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