Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions
Abstract This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of the properties of Hilfer fractional calculus, the theory of propagation families as well as the theory of the measure of noncompactness and fixed p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-0965-3 |
| _version_ | 1828855027392839680 |
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| author | Haide Gou Baolin Li |
| author_facet | Haide Gou Baolin Li |
| author_sort | Haide Gou |
| collection | DOAJ |
| description | Abstract This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of the properties of Hilfer fractional calculus, the theory of propagation families as well as the theory of the measure of noncompactness and fixed point methods, we obtain the existence results of mild solutions for Sobolev-type fractional evolution differential equations involving the Hilfer fractional derivative. Finally, an example is presented to illustrate the main result. |
| first_indexed | 2024-12-13T00:47:03Z |
| format | Article |
| id | doaj.art-9df7821fb4c546fba3fc580b9c89eb33 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T00:47:03Z |
| publishDate | 2018-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-9df7821fb4c546fba3fc580b9c89eb332022-12-22T00:05:01ZengSpringerOpenBoundary Value Problems1687-27702018-04-012018112510.1186/s13661-018-0965-3Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditionsHaide Gou0Baolin Li1College of Mathematics and Statistics, Northwest Normal UniversityCollege of Mathematics and Statistics, Northwest Normal UniversityAbstract This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of the properties of Hilfer fractional calculus, the theory of propagation families as well as the theory of the measure of noncompactness and fixed point methods, we obtain the existence results of mild solutions for Sobolev-type fractional evolution differential equations involving the Hilfer fractional derivative. Finally, an example is presented to illustrate the main result.http://link.springer.com/article/10.1186/s13661-018-0965-3Evolution equationsMild solutionsHilfer fractional derivativeNoncompact measure |
| spellingShingle | Haide Gou Baolin Li Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions Boundary Value Problems Evolution equations Mild solutions Hilfer fractional derivative Noncompact measure |
| title | Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions |
| title_full | Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions |
| title_fullStr | Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions |
| title_full_unstemmed | Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions |
| title_short | Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions |
| title_sort | existence of mild solutions for sobolev type hilfer fractional evolution equations with boundary conditions |
| topic | Evolution equations Mild solutions Hilfer fractional derivative Noncompact measure |
| url | http://link.springer.com/article/10.1186/s13661-018-0965-3 |
| work_keys_str_mv | AT haidegou existenceofmildsolutionsforsobolevtypehilferfractionalevolutionequationswithboundaryconditions AT baolinli existenceofmildsolutionsforsobolevtypehilferfractionalevolutionequationswithboundaryconditions |