The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.
In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.
AbstractA Search/Matcti program lias 'beea written for the IBM PC AT computer that is capable of -using "background - subtracted, digitized 2-ray powder diffraction scans as inputs in addition to the d/I data traditionally used. This novel procedure has proved especially effective when numerous unresolved lines are present in the pattern. The method is also less demanding of data quality thaii the peak location programs. The program may he extended to searching & data "base of digitized standard patterns.The program, has several parameters that can- "be adjusted, including chemistry. The results from the Johnson/Vand list type of output are directly accessible to the interactive graphics program. This gives the diffraction!st a fast method for verifying the phase identification. Because of the speed of fixed point computation techniques, the 52,791 pattern file can be scanned in about 90 seconds.This paper will illustrate the utility of the program.
Fixed point (especially, the minimum norm fixed point) computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings.
In an abstract framework, we consider the following initial value problem: u′′ + μAu + F(u)u = f in (0,T), u(0)=u0,u′(0)=u1, where μ is a positive function and f a nonsmooth function. Given u0, u1, and f we determine Fu in order to have a solution u of the previous equation. We analyze two cases of Fu. In our approach, we use the Theory of Linear Operators in Hilbert Spaces, the compactness Aubin-Lions Theorem, and an argument of Fixed Point. One of our two results provides an answer in a certain sense to an open question formulated by Lions in (1981, Page 284).
Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations
