In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...

We provide solution of first order linear fuzzy differential equations by variation of constant formula. The differentiability concept used in this paper is the strongly generalized differentiability since a fuzzy differential equation under this differentiability can have decreasing legth of support function. Under some conditions we provide solution with decreasing support and so the behaviou...

Peano differentiability generalizes ordinary differentiability to higher order. There are two ways to define Peano differentiability for functions defined on non-open sets. For both concepts, we investigate the question under which conditions a function defined on a closed set can be extended to a Peano differentiable function on the ambient space if the sets and functions are definable in an o...

Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

Recently, in their paper, the authors generalized notion of differentiability by defining it for all points functional domain (not only interior points) which can be considered meaningful. In this continuous is introduced differentiable function f:X→Rm with a not necessarily open X⊆Rn; i.e., continuity mapping df:X→HomRn,Rm considered. addition to introducing context approach differentiability,...

This study examines the nature of media bias within the news media (for this study, newspapers and television news), the trajectories and methods through which these biases are spread and how a hegemony is formed, and looks at the qualities of this hegemony. The thesis begins with a review of some of the literature covering bias in the news media, approaching the issue from a number of angles a...

This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive and negative fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, con...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

In this paper, we present a numerical computational approach for solving Caputo type fractional differential equations. This method is based on approximation of Caputo derivative in terms of integer order derivatives and waveform relaxation method. The utility of the method is shown by applying it to several examples. A comparative study indicates that our approach is more efficient and accurat...

There has been a recent increase in interest in the use of distributed order differential equations (particularly in the case where the derivatives are given in the Caputo sense) to model various phenomena. Recent papers have provided insights into the numerical approximation of the solution, and some results on existence and uniqueness have been proved. In each case, the representation of the ...