‐maximal regularity for fractional difference equations on UMD spaces |
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Authors: | Carlos Lizama |
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Institution: | Universidad de Santiago de Chile, Facultad de Ciencia, Departamento de Matemática y Ciencia de la Computación, Estación Central, Santiago |
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Abstract: | Let T be a bounded linear operator defined on a Banach space X. We introduce an operator theoretical method for linear fractional difference equations based on the notion of α‐resolvent sequence of bounded and linear operators. Then, we define and characterize the ‐ maximal regularity of solutions for the problem solely in terms of the R‐boundedness of the set ![urn:x-wiley:0025584X:media:mana201400326:mana201400326-math-0005 urn:x-wiley:0025584X:media:mana201400326:mana201400326-math-0005]() |
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Keywords: | Fractional differences maximal regularity UMD spaces R‐boundedness 39A06 39A12 43A15 |
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