Abstract
We introduce the concept of α times C-second resolvent families and present the relationship between α times C-resolvent families and α times C-second resolvent families. Moreover, the perturbation and square root for α times C-resolvent families are considered in this paper which generalize the counterparts of C-Cosine operator functions.
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The first author is supported by NSF of China (Grant No. 10971146); the second and the third authors are supported by NSF of China (Grant No. 10671205) and the Science & Technology Project of Xuzhou City (Grant No. XM08C095)
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Chen, C., Song, X.Q. & Li, H.M. The reduction square root and perturbation for a class of strongly continuous operator families. Acta. Math. Sin.-English Ser. 26, 1993–2002 (2010). https://doi.org/10.1007/s10114-010-7644-3
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DOI: https://doi.org/10.1007/s10114-010-7644-3
Keywords
- Fractional calculus
- α times C-resolvent families
- α times C-second resolvent families
- Laplace transforms
- fractional evolution equations