Abstract We know that interpolation spaces in terms of analytic semigroup have a significant role into the study strict Hölder regularity solutions classical abstract Cauchy problem (ACP). In this paper, we first construct solution operators fractional calculus and characterize these spaces. Then establish mild order ACP.

A classical theory is developed for the time development and scattering of a minimally coupled scalar eld on closed spacetimes that evolve from initial, to nal static states. The time development is obtained by reformulating the eld equation as an abstract Cauchy problem on a Hilbert space. Constraints are imposed on the metric that enable the use of semigroup theory, and the eld solution is ob...

This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d    with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(&lambda1, &lambda2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(&lambda)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(&lambd...