in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

To match the observed patterns of protection over business cycle, I add unemployment into two models of trade policy: ‘Protection for Sale’(1994) and ‘Trade Wars and Trade Talks’(1995) by Grossman and Helpman. The source of unemployment is …nancial frictions: as in Aghion et.al. (2009) …rms with pro…ts less than a random threshold are liquidated. With small shocks protection goes up to save emp...

FDI has received surprisingly little attention in theoretical and empirical work on openness and growth. This paper presents a theoretical growth model where MNCs directly affect the endogenous growth rate via technological spillovers. This is novel since other endogenous growth models with MNCs, e.g. the Grossman-Helpman model, assume away the knowledge-spillovers aspect of FDI. We also presen...

In a recent paper Helpman, Melitz and Yeaple (2002) argue firm heterogeneity leads to self-selection in the structure of international commerce. Only the most productive firms find it profitable to meet the higher costs associated with FDI; the next set of firms find it profitable to serve foreign markets through exporting; while the least productive firms find it profitable to serve only domes...

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...