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- W2981226960 abstract "In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $D^{alpha}_Cu(t)=Au(t)+f(t)$ on the half line, where $D^{alpha}_Cu(t)$ is the derivative of the function $u$ in Caputo's sense, $A$ is generally an unbounded closed operator, $f$ is polynomially bounded. To this end we develop a spectral theory for functions of polynomial growth on the half line. Our main result claims that if $u$ is mild solution of the Cauchy problem such that $lim_{hdownarrow 0} sup_{tge 0} | u(t+h)-u(t)|/(1+t)^n=0$, and $sup_{tge 0} | u(t)| /(1+t)^n <infty$, then, $lim_{ttoinfty} u(t)/(1+t)^n =0$ provided that the spectral set $Sigma (A,alpha )cap iR$ is countable, where $Sigma (A,alpha )$ is defined to be the set of complex numbers $xi$ such that $lambda^{alpha -1} (lambda^alpha -A)^{-1}$ is analytic in a neighborhood of $xi$, and $u$ satisfies some ergodic" @default.
- W2981226960 created "2019-10-25" @default.
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- W2981226960 date "2019-10-18" @default.
- W2981226960 modified "2023-09-23" @default.
- W2981226960 title "Asymptotic Behavior of Polynomially Bounded Solutions of Linear Fractional Differential Equations" @default.
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