Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method
This paper is concerned with the study of nonlocal fractional differential equation of sobolev type with impulsive conditions. An associated integral equation is obtained and then considered a sequence of approximate integral equations. By utilizing the techniques of Banach fixed point approach and...
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023229?viewType=HTML |
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| author | M. Manjula K. Kaliraj Thongchai Botmart Kottakkaran Sooppy Nisar C. Ravichandran |
| author_facet | M. Manjula K. Kaliraj Thongchai Botmart Kottakkaran Sooppy Nisar C. Ravichandran |
| author_sort | M. Manjula |
| collection | DOAJ |
| description | This paper is concerned with the study of nonlocal fractional differential equation of sobolev type with impulsive conditions. An associated integral equation is obtained and then considered a sequence of approximate integral equations. By utilizing the techniques of Banach fixed point approach and analytic semigroup, we obtain the existence and uniqueness of mild solutions to every approximate solution. Then, Faedo-Galerkin approximation is used to establish certain convergence outcome for approximate solutions. In order to illustrate the abstract results, we present an application as a conclusion. |
| first_indexed | 2024-04-10T21:41:04Z |
| format | Article |
| id | doaj.art-1a136ef18d9d45408fad70ec96327619 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T21:41:04Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-1a136ef18d9d45408fad70ec963276192023-01-19T01:31:55ZengAIMS PressAIMS Mathematics2473-69882023-01-01824645466510.3934/math.2023229Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function methodM. Manjula 0K. Kaliraj1Thongchai Botmart 2Kottakkaran Sooppy Nisar3 C. Ravichandran41. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamil Nadu, India1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamil Nadu, India2. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand3. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia4. Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, IndiaThis paper is concerned with the study of nonlocal fractional differential equation of sobolev type with impulsive conditions. An associated integral equation is obtained and then considered a sequence of approximate integral equations. By utilizing the techniques of Banach fixed point approach and analytic semigroup, we obtain the existence and uniqueness of mild solutions to every approximate solution. Then, Faedo-Galerkin approximation is used to establish certain convergence outcome for approximate solutions. In order to illustrate the abstract results, we present an application as a conclusion.https://www.aimspress.com/article/doi/10.3934/math.2023229?viewType=HTMLfractional calculusimpulsivefixed point techniquessobolev type |
| spellingShingle | M. Manjula K. Kaliraj Thongchai Botmart Kottakkaran Sooppy Nisar C. Ravichandran Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method AIMS Mathematics fractional calculus impulsive fixed point techniques sobolev type |
| title | Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method |
| title_full | Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method |
| title_fullStr | Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method |
| title_full_unstemmed | Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method |
| title_short | Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, blow-up, test function method |
| title_sort | moore gibson thompson equation general initial values nonlinear memory terms blow up test function method |
| topic | fractional calculus impulsive fixed point techniques sobolev type |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023229?viewType=HTML |
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