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Applied Mathematics(A Journal of Chinese Universities) 2022年第2期37卷 228-245页

作者： WEI Mei LI Qiang Department of Mathematics Northwest Normal UniversityLanzhou 730070China Department of Mathematics Shanxi Normal UniversityLinfen 041000China School of Mathematical Sciences Qufu Normal UniversityQufu 273165China

In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.

关键词： neutral fractional evolution equations S-asymptotically periodic problem α-mild solutions fractional power space analytic semigroup

Existence of p-mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation

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Acta Mathematicae Applicatae Sinica 2021年第3期37卷 645-656页

作者： Xiao-ke SUN Ping HE School of Mathematics Shanghai University of Finance and EconomicsShanghai200433China

A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.

关键词： p-mean almost periodic solution fractional stochastic neutral functional differential equation fixed point theorem sectorial operator analytic semigroup

Distances between Elements of a semigroup and Estimates for Derivatives

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2239-2254页

作者： Zohra BENDOUAD Isabelle CHALENDAR Jean ESTERLE Jonathan R.PARTINGTON Université Amar Telidji Laboratoire de Sciences Economiques et Sciences de Gestion Université de Lyon CNRS Université Lyon 1 Institut Camille Jordan L.A.B.A. G Université Bordeaux 1 351 cours de la Libération School of Mathematics University of Leeds

This paper is concerned first with the behaviour of differences T（t） - T（s） near the origin, where （T（t）） is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane （in which case it is assumed analytic）. For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T（t） -T（2t） have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator.

关键词： semigroup of operators analytic semigroup Banach algebras non-quasinilpotent quasinilpotent

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 2011年第3期27卷 318-322页

作者： Heping Jiang(Dept. of Math.,Huangshan University,Huangshan 245041,Anhui) Wei Jiang(School of Mathematical Science,University of Anhui,Hefei 230039)

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.

关键词： mild solutions fractional order functional differential equations Banach fixed point theorem analytic semigroup