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.

Let X be a connected topological space and c∈H2(X;Z) non-zero cohomology class. A Homeo(X,c)-bundle is fiber bundle with whose structure group reduces to the Homeo(X,c) of c-preserving homeomorphisms X. If H1(X;Z)=0, then characteristic class for Homeo(X,c)-bundles called Dixmier-Douady defined via Serre spectral sequence. We show relation between universal foliated gauge extension Homeo(X,c). ...

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...

Abstract Let $K$ denote either ${\mathbb{R}}$ or ${\mathbb{C}}$. In this article, we study two new equivariants and a invariant attached to rational map $f\in K(z)$ under the action of conjugation by ${\operatorname{SL}}_2(K)$. The 1st naturally live on real hyperbolic $[K:{\mathbb{Q}}]+1$ space carry information about $f$ ${\mathbb{P}}^1(K)$. When $K={\mathbb{C}}$, how these objects behave as ...

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...

| We give a new proof that all external rays of the Man-delbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is diierent from the original one, given by Douady and Hubbard and reened by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depe...

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...