Almost automorphic mild solutions to fractional partial difference-differential equations

作者：Abadias Luciano; Lizama Carlos

来源：APPLICABLE ANALYSIS, 2016, 95(6): 1347-1369.

DOI：10.1080/00036811.2015.1064521

• 43A60
• 35R11
• 47D06
• 34A08
• Weyl-like fractional difference
• almost automorphic sequence
• mild solution
• -semigroups
• fractional difference equations

We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as
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for
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where
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is the generator of a
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-semigroup defined on a Banach space
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,
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denote fractional difference in Weyl-like sense and
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satisfies Lipchitz conditions of global and local type. We introduce the notion of
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-resolvent sequence
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and we prove that a mild solution of
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corresponds to a fixed point of
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We show that such mild solution is strong in case of the forcing term belongs to an appropriate weighted Lebesgue space of sequences. Application to a model of population of cells is given.

• 出版日期2016-6-2