Abstract This paper is mainly concerned with a controlled multi-term fractional evolution equation in Banach spaces. Firstly, we give formula of its mild solutions and show the existence result for problem via $\omega $-sectorial operator technique. Secondly, establish Lagrange optimal control time system invoked by nonlocal Cauchy problems properties resolvent operators.

Abstract We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides manifolds with infinite cylindrical ends. show that if the cut-off resolvent is polynomially bounded at high energies, as case in certain favorable geometries, then there an asymptotic expansion, up a $O(t^{-k_0})$ remainder, of solutions equation on compact sets $t \to \infty $. In mo...

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

This note covers various aspects of recent attempts to describe membranes ending on fivebranes using fuzzy geometry. In particular, we examine the Basu-Harvey equation and its relation to the Nahm equation as well as the consequences of using a non-associative algebra for the fuzzy three-sphere. This produces the tantalising result that the fuzzy funnel solution corresponding to Q coincident me...

We study the asymptotic behavior of solutions nonlinear fractional evolution equations in Banach spaces. Asymptotically almost periodic on half line are obtained by establishing a sharp estimate resolvent operator family equations. In particular, when semigroup generated A is exponentially stable then conditions existence asymptotically satisfied. An application to partial differential equation...

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

We consider the transmission problem for second-order diierential equations with unbounded interfaces. The spaces B and B are used to prove the limiting absorption principle for the steady-state problem and to establish the resolvent estimate at low frequencies for the steady-state operator. These are then applied in showing the validity of the limiting amplitude principle for such an operator....

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient accurate approximations can be obtained using well-...

the pioneer work of image compression/reconstruction based onfuzzy relational equations (icf) and the related works are introduced. theicf regards an original image as a fuzzy relation by embedding the brightnesslevel into [0,1]. the compression/reconstruction of icf correspond to thecomposition/solving inverse problem formulated on fuzzy relational equations.optimizations of icf can be consequ...

in this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. weshow that obtained result is an extension of the result ofrodr'{i}guez-l'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.