Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay
Abstract In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1526-5 |
| _version_ | 1824008441865175040 |
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| author | Haide Gou Baolin Li |
| author_facet | Haide Gou Baolin Li |
| author_sort | Haide Gou |
| collection | DOAJ |
| description | Abstract In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on an operator family generated by the operator pair ( A , B ) $(A,B)$ and probability density function. Combining the techniques of fractional calculus, measure of noncompactness, and fixed point theorem with respect to k-set-contractive, we obtain a new existence result of mild solutions. The results obtained improve and extend some related conclusions on this topic. At last, we present an application that illustrates the abstract results. |
| first_indexed | 2024-12-18T20:57:17Z |
| format | Article |
| id | doaj.art-c63df0ab71554d9989476353f8ef1e74 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-18T20:57:17Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-c63df0ab71554d9989476353f8ef1e742022-12-21T20:53:11ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-10-012017112010.1186/s13660-017-1526-5Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delayHaide Gou0Baolin Li1College of Mathematics and Statistics, Northwest Normal UniversityCollege of Mathematics and Statistics, Northwest Normal UniversityAbstract In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on an operator family generated by the operator pair ( A , B ) $(A,B)$ and probability density function. Combining the techniques of fractional calculus, measure of noncompactness, and fixed point theorem with respect to k-set-contractive, we obtain a new existence result of mild solutions. The results obtained improve and extend some related conclusions on this topic. At last, we present an application that illustrates the abstract results.http://link.springer.com/article/10.1186/s13660-017-1526-5evolution equationsmild solutionsHilfer fractional derivativenoncompact measure |
| spellingShingle | Haide Gou Baolin Li Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay Journal of Inequalities and Applications evolution equations mild solutions Hilfer fractional derivative noncompact measure |
| title | Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay |
| title_full | Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay |
| title_fullStr | Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay |
| title_full_unstemmed | Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay |
| title_short | Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay |
| title_sort | existence of mild solutions for fractional nonautonomous evolution equations of sobolev type with delay |
| topic | evolution equations mild solutions Hilfer fractional derivative noncompact measure |
| url | http://link.springer.com/article/10.1186/s13660-017-1526-5 |
| work_keys_str_mv | AT haidegou existenceofmildsolutionsforfractionalnonautonomousevolutionequationsofsobolevtypewithdelay AT baolinli existenceofmildsolutionsforfractionalnonautonomousevolutionequationsofsobolevtypewithdelay |