Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems
In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5729128 |
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| _version_ | 1832551689812443136 |
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| author | Mohamed Hannabou Khalid Hilal Ahmed Kajouni |
| author_facet | Mohamed Hannabou Khalid Hilal Ahmed Kajouni |
| author_sort | Mohamed Hannabou |
| collection | DOAJ |
| description | In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered. |
| format | Article |
| id | doaj-art-9a96202d6eb148c89543b316711464a4 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9a96202d6eb148c89543b316711464a42025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/57291285729128Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy ProblemsMohamed Hannabou0Khalid Hilal1Ahmed Kajouni2Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Université Sultan Moulay Slimane, 23000 Beni Mellal, MoroccoLaboratoire de Mathématiques Appliquées & Calcul Scientifique, Université Sultan Moulay Slimane, 23000 Beni Mellal, MoroccoLaboratoire de Mathématiques Appliquées & Calcul Scientifique, Université Sultan Moulay Slimane, 23000 Beni Mellal, MoroccoIn this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.http://dx.doi.org/10.1155/2020/5729128 |
| spellingShingle | Mohamed Hannabou Khalid Hilal Ahmed Kajouni Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems Journal of Mathematics |
| title | Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems |
| title_full | Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems |
| title_fullStr | Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems |
| title_full_unstemmed | Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems |
| title_short | Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems |
| title_sort | existence and uniqueness of mild solutions to impulsive nonlocal cauchy problems |
| url | http://dx.doi.org/10.1155/2020/5729128 |
| work_keys_str_mv | AT mohamedhannabou existenceanduniquenessofmildsolutionstoimpulsivenonlocalcauchyproblems AT khalidhilal existenceanduniquenessofmildsolutionstoimpulsivenonlocalcauchyproblems AT ahmedkajouni existenceanduniquenessofmildsolutionstoimpulsivenonlocalcauchyproblems |