Resolvent Positive Operators and Positive Fractional Resolvent Families
This paper is concerned with positive α-times resolvent families on an ordered Banach space E (with normal and generating cone), where 0<α≤2. We show that a closed and densely defined operator A on E generates a positive exponentially bounded α-times resolvent family for some 0<α<1 if and o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6418846 |
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| Summary: | This paper is concerned with positive α-times resolvent families on an ordered Banach space E (with normal and generating cone), where 0<α≤2. We show that a closed and densely defined operator A on E generates a positive exponentially bounded α-times resolvent family for some 0<α<1 if and only if, for some ω∈ℝ, when λ>ω,λ∈ρA, Rλ,A≥0 and supλRλ,A: λ≥ω<∞. Moreover, we obtain that when 0<α<1, a positive exponentially bounded α-times resolvent family is always analytic. While A generates a positive α-times resolvent family for some 1<α≤2 if and only if the operator λα−1λα−A−1 is completely monotonic. By using such characterizations of positivity, we investigate the positivity-preserving of positive fractional resolvent family under positive perturbations. Some examples of positive solutions to fractional differential equations are presented to illustrate our results. |
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| ISSN: | 2314-8896 2314-8888 |