Asymptotically Almost Periodicity for a Class of Weyl–Liouville fractional Evolution Equations View Full Text


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Article Info

DATE

2018-08

AUTHORS

Junfei Cao, Amar Debbouche, Yong Zhou

ABSTRACT

This paper is devoted to study a class of abstract fractional evolution equation in a Banach space X: 1D+αx(t)+Ax(t)=F(t,x(t)),t∈R,where 0<α<1, -A is the infinitesimal generator of a C0-semigroup on X, and F(t, x) is an appropriate function defined on phase space; the fractional derivative is understood in the Weyl–Liouville sense. Combining the fixed point theorem due to Krasnoselskii and a decomposition technique, we obtain some new sufficient conditions to ensure the existence of asymptotically almost periodic mild solutions for (1). Our result generalizes and improves some previous results, since the Lipschitz continuity on the nonlinearity F(t, x) with respect to x is not required. An example is also presented as an application to illustrate the feasibility of the abstract result. More... »

PAGES

155

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00009-018-1208-7

DOI

http://dx.doi.org/10.1007/s00009-018-1208-7

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https://app.dimensions.ai/details/publication/pub.1104694375


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