Scientific Research Publishing

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53678#.VM8xcSzQrzE Author(s)   Vladimir V. Uchaikin Affiliation(s) Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk, Russia . ABSTRACT Studying the cosmic ray transport in the Galaxy, we deal with two interacting substances: charged particles and interstellar magnetic field. Two coupled local equations describe this complicated system, but elimination of one of them (say, the magnetic field equation) transforms remaining one (the cosmic rays equation) into the nonlocal form. The most popular nonlocal operators in the cosmic ray physics are integro-differential operators of fractional order. This report contains review of recent works in this direction, including original results of the author. In the last section, some specific problems are discussed: fractional operators with soft truncation of their kernels, nonlocal properties of fractiona...

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53065#.VLSP-cnQrzE Author(s)    Dhiman Bose , Uma Basu Affiliation(s) Department of Applied Mathematics, University of Calcutta, Calcutta, India . ABSTRACT In this paper an attempt has been made to study the unsteady incompressible flow of a generalized Oldroyd-B fluid between two oscillating parallel plates in presence of a transverse magnetic field. An exact solution for the velocity field has been obtained by means of Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. The dependence of the velocity field on fractional as well as material parameters has been illustrated graphically. The velocity fields for the classical Newtonian, generalized Maxwell, generalized second grade and ordinary Oldroyd-B fluids are recovered as limiting cases of the flow considered for the generalized Oldroyd-B fluid. ...