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.

Abstract We propose a general framework for quantum walks on d -dimensional spaces. investigate asymptotic behavior of these walks. prove that every homogeneous with finite degree freedom have limit distribution. This theorem can also be applied to crystal lattice. In this theorem, it is not necessary assume the support initial unit vector finite. pay attention 1-cocycles, which related Heisenb...

In this note we are concerned with fixed point theory for holomorphic self maps on complex manifolds. After the well-known Schwarz lemma on the unit disk, which assumes a fixed point, the Pick theorem was proved in [8]. This can be extended to a Pick-type theorem on hyperbolic Riemann surfaces as is shown in [5, 7]. For a more general type of space: open, connected and bounded subsets of a Bana...

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 ...

Top-down theorem provers with depth-rst search (e.g., PTTP [Sti88], METEOR [AL91], SETHEO [LSBB92]) have the general disadvantage that during the search the same goals have to be proven over and over again, thus causing a large amount of redundancy. Resolution-based bottom-up theorem provers (e.g., OTTER [McC90]), on the other hand, avoid this problem by performing backward and forward subsumpt...

Abstract Let ϕ be a normalized convex function defined on open unit disk D . For unified class of analytic functions which satisfy the second order differential subordination f′ ( z ) + αzf″ ≺ for all z ∈ , we investigate distortion theorem and grow...

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...