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Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem

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  • Ya-Ning Li
  • Hong-Rui Sun

Abstract

We firstly prove that -times integrated -resolvent operator function ( -ROF) satisfies a functional equation which extends that of -times integrated semigroup and -resolvent operator function. Secondly, for the inhomogeneous -Cauchy problem , , , if is the generator of an -ROF, we give the relation between the function and mild solution and classical solution of it. Finally, for the problem , , , where is a linear closed operator. We show that generates an exponentially bounded -ROF on a Banach space if and only if the problem has a unique exponentially bounded classical solution and Our results extend and generalize some related results in the literature.

Suggested Citation

  • Ya-Ning Li & Hong-Rui Sun, 2014. "Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, January.
    • Handle: RePEc:hin:jnlaaa:430418
    DOI: 10.1155/2014/430418
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