abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

We investigate the dynamics of the recently proposed model of assisted inflation. In this model an arbitrary number of scalar fields with exponential potentials evolve towards an inflationary scaling solution, even if each of the individual potentials is too steep to support inflation on its own. By choosing an appropriate rotation in field space we can write down explicitly the potential for t...

a generalization of schauder basis associated with the concept of generalized analytic functions is introduced. corresponding concepts of density, completeness, biorthogonality and basicity are defined. also, corresponding concept of the space of coefficients is introduced. under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...