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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| Format: | Article |
| Language: | English |
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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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| author | Nan-Ding Li Ru Liu Miao Li |
| author_facet | Nan-Ding Li Ru Liu Miao Li |
| author_sort | Nan-Ding Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d0fa4d91d7c241f8855d96bbde5b60f0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d0fa4d91d7c241f8855d96bbde5b60f02025-02-03T01:25:08ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/64188466418846Resolvent Positive Operators and Positive Fractional Resolvent FamiliesNan-Ding Li0Ru Liu1Miao Li2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaCollege of Computer Science, Chengdu University, Chengdu, Sichuan 610106, ChinaDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaThis 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.http://dx.doi.org/10.1155/2021/6418846 |
| spellingShingle | Nan-Ding Li Ru Liu Miao Li Resolvent Positive Operators and Positive Fractional Resolvent Families Journal of Function Spaces |
| title | Resolvent Positive Operators and Positive Fractional Resolvent Families |
| title_full | Resolvent Positive Operators and Positive Fractional Resolvent Families |
| title_fullStr | Resolvent Positive Operators and Positive Fractional Resolvent Families |
| title_full_unstemmed | Resolvent Positive Operators and Positive Fractional Resolvent Families |
| title_short | Resolvent Positive Operators and Positive Fractional Resolvent Families |
| title_sort | resolvent positive operators and positive fractional resolvent families |
| url | http://dx.doi.org/10.1155/2021/6418846 |
| work_keys_str_mv | AT nandingli resolventpositiveoperatorsandpositivefractionalresolventfamilies AT ruliu resolventpositiveoperatorsandpositivefractionalresolventfamilies AT miaoli resolventpositiveoperatorsandpositivefractionalresolventfamilies |