Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative
In this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Secon...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2022/3386198 |
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| _version_ | 1832549575827652608 |
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| author | Khalid Hilal Ahmed Kajouni Hamid Lmou |
| author_facet | Khalid Hilal Ahmed Kajouni Hamid Lmou |
| author_sort | Khalid Hilal |
| collection | DOAJ |
| description | In this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on Krasnoselskii’s fixed point, and to deal with the uniqueness result, we use Banach’s contraction principle. Third of all, in the inclusion case, to obtain the existence result, we use the Leray–Schauder alternative. Last but not least, we give an illustrative example. |
| format | Article |
| id | doaj-art-5943426138184c07b23149fcf04e7b42 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-5943426138184c07b23149fcf04e7b422025-02-03T06:10:55ZengWileyInternational Journal of Differential Equations1687-96512022-01-01202210.1155/2022/3386198Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional DerivativeKhalid Hilal0Ahmed Kajouni1Hamid Lmou2Laboratory of Applied Mathematics and Scientific CompetingLaboratory of Applied Mathematics and Scientific CompetingLaboratory of Applied Mathematics and Scientific CompetingIn this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on Krasnoselskii’s fixed point, and to deal with the uniqueness result, we use Banach’s contraction principle. Third of all, in the inclusion case, to obtain the existence result, we use the Leray–Schauder alternative. Last but not least, we give an illustrative example.http://dx.doi.org/10.1155/2022/3386198 |
| spellingShingle | Khalid Hilal Ahmed Kajouni Hamid Lmou Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative International Journal of Differential Equations |
| title | Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative |
| title_full | Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative |
| title_fullStr | Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative |
| title_full_unstemmed | Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative |
| title_short | Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative |
| title_sort | boundary value problem for the langevin equation and inclusion with the hilfer fractional derivative |
| url | http://dx.doi.org/10.1155/2022/3386198 |
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