A study of nonlocal fractional delay differential equations with hemivariational inequality
In this paper, we study an abstract system of fractional delay differential equations of order $ 1 < q < 2 $ with a hemivariational inequality in Banach spaces. To establish the existence of a solution to the abstract inequality, we employ the Rothe technique in conjunction with the su...
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AIMS Press
2023-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023659?viewType=HTML |
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| author | Ebrahem A. Algehyne Abdur Raheem Mohd Adnan Asma Afreen Ahmed Alamer |
| author_facet | Ebrahem A. Algehyne Abdur Raheem Mohd Adnan Asma Afreen Ahmed Alamer |
| author_sort | Ebrahem A. Algehyne |
| collection | DOAJ |
| description | In this paper, we study an abstract system of fractional delay differential equations of order $ 1 < q < 2 $ with a hemivariational inequality in Banach spaces. To establish the existence of a solution to the abstract inequality, we employ the Rothe technique in conjunction with the surjectivity of multivalued pseudomonotone operators and features of the Clarke generalized gradient. Further, to show the existence of the fractional differential equation, we use the fractional cosine family and fixed point theorem. Finally, we include an example to elaborate the effectiveness of the findings. |
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| format | Article |
| id | doaj.art-6ccfdf75d5944cfca5f5cbcce4e0f27f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T18:24:20Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6ccfdf75d5944cfca5f5cbcce4e0f27f2023-04-12T01:21:55ZengAIMS PressAIMS Mathematics2473-69882023-04-0186130731308710.3934/math.2023659A study of nonlocal fractional delay differential equations with hemivariational inequalityEbrahem A. Algehyne0Abdur Raheem1Mohd Adnan2Asma Afreen 3Ahmed Alamer41. Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia2. Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India2. Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India2. Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India1. Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi ArabiaIn this paper, we study an abstract system of fractional delay differential equations of order $ 1 < q < 2 $ with a hemivariational inequality in Banach spaces. To establish the existence of a solution to the abstract inequality, we employ the Rothe technique in conjunction with the surjectivity of multivalued pseudomonotone operators and features of the Clarke generalized gradient. Further, to show the existence of the fractional differential equation, we use the fractional cosine family and fixed point theorem. Finally, we include an example to elaborate the effectiveness of the findings.https://www.aimspress.com/article/doi/10.3934/math.2023659?viewType=HTMLcaputo fractional derivativehemivariational inequalityrothe methodclarke subdifferentialpseudomonotone |
| spellingShingle | Ebrahem A. Algehyne Abdur Raheem Mohd Adnan Asma Afreen Ahmed Alamer A study of nonlocal fractional delay differential equations with hemivariational inequality AIMS Mathematics caputo fractional derivative hemivariational inequality rothe method clarke subdifferential pseudomonotone |
| title | A study of nonlocal fractional delay differential equations with hemivariational inequality |
| title_full | A study of nonlocal fractional delay differential equations with hemivariational inequality |
| title_fullStr | A study of nonlocal fractional delay differential equations with hemivariational inequality |
| title_full_unstemmed | A study of nonlocal fractional delay differential equations with hemivariational inequality |
| title_short | A study of nonlocal fractional delay differential equations with hemivariational inequality |
| title_sort | study of nonlocal fractional delay differential equations with hemivariational inequality |
| topic | caputo fractional derivative hemivariational inequality rothe method clarke subdifferential pseudomonotone |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023659?viewType=HTML |
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