Applications of fractional calculus techniques to problems in biophysics (Q2773692)

This article begins with a review of dynamical complexity of physical and biophysical systems. Further, Riemann-Liouville fractional differentials and integrals are described. Next, Maxwell-Debye relaxation and non-Debye relaxation processes are discussed. Further, the fractional integral and differential equations on the Zwanzig's projection formalism for a power law memory kernel are derived. Another physical basis to come up with memory is Boltzmann's superposition principle which formally incorporates memory through phenomenological casual convolution.NEWLINENEWLINENEWLINENext, Markov chains and Bernoulli scaling in ion channelling are demonstrated. A brief review of fractional constitutive rheological models is also given. It is indicated that the Glöckle and Nonnenmacher model [Macromolecules (1991)] is used to explain data from filled polymers [J. Chem. Phys. 103, 7180 ff (1995)]. Results for equilibrium modulus and fractional protein dynamics are depicted by drawing various graphs. The section on anomalous diffusions contains a description of Fickean diffusions, Cattaneo diffusions and the generalized diffusion equation due to Metzler et al. [Physica 211 A, 13 ff (1994)], spectral transforms, fluorescence recovery, etc. Finally, the appendix involves stable laws, properties of Fox's \(H\)-function and fractal Fourier transforms.NEWLINENEWLINENEWLINEA detailed and comprehensive account of Fox's \(H\)-function is available from the monograph of \textit{A.M. Mathai} and the reviewer, The \(H\)-function with applications in statistics and other disciplines (1978; Zbl 0382.33001).NEWLINENEWLINEFor the entire collection see [Zbl 0998.26002].