‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

We show that solving the problem of baryon-number violation in nonsupersymmetric grand unified theories (GUT's) in warped higher-dimensional spacetime can lead to a stable Kaluza-Klein particle. This exotic particle has gauge quantum numbers of a right-handed neutrino, but carries fractional baryon number and is related to the top quark within the higher-dimensional GUT. A combination of baryon...

Cell movement--for example, during embryogenesis or tumor metastasis--is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating cells resemble those of thermally driven Brownian particles. However, cell migration is an active biological process putting a characterization in terms of nor...

In this paper, we show how to construct some explicit modular forms of weight 4/5 for Γ(11). We first compute the group of all invariant line bundles on the modular curve of level p. We then show that many modular forms of certain fractional weights occur in nature, using work of Felix Klein and our computation of the invariant line bundles. Using Klein’s work, the Woods Hole Fixed Point Formul...

Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution the potential can take advantage fractional moment method introduced by Aizenman-Molchanov, or use classical Wegner estimate as part another method, e.g. multi-scale analysis Fr\"ohlich-Spencer and significantly developed Klein his collaborators. When is singular, most proofs rely crucially on expon...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

monte carlo simulation is widely used in calculations involing transport of photons through different materials of different shapes. the method consists of randomly generating a finite set of photon histories over which the quantities of interest are averaged. in photon transport calculations, sampling the photon scattering angle from the klein-nishina probability distribution is of special imp...