Study of time fractional order problems with proportional delay and controllability term via fixed point approach
In the current manuscript, we are tying to study one of the important class of differential equations known is evolution equations. Here, we considered the problem under controllability term and with proportional delay. Before going to numerical or analytical solution it is important to check the ex...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021317?viewType=HTML |
| _version_ | 1818677597106601984 |
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| author | Muhammad Sher Kamal Shah Zareen A. Khan |
| author_facet | Muhammad Sher Kamal Shah Zareen A. Khan |
| author_sort | Muhammad Sher |
| collection | DOAJ |
| description | In the current manuscript, we are tying to study one of the important class of differential equations known is evolution equations. Here, we considered the problem under controllability term and with proportional delay. Before going to numerical or analytical solution it is important to check the existence and uniqueness of the solution. So, we will consider our problem for qualitative theory using fixed point theorems of Banach's and Krasnoselskii's type. For numerical solution the stability is important, hence the problem is also studied for Ulam-Hyer's type stability. At the end an example is constructed to ensure the establish results. |
| first_indexed | 2024-12-17T09:01:54Z |
| format | Article |
| id | doaj.art-45d422a5a78346e5a093c8f9e12bc193 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T09:01:54Z |
| publishDate | 2021-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-45d422a5a78346e5a093c8f9e12bc1932022-12-21T21:55:40ZengAIMS PressAIMS Mathematics2473-69882021-03-01655387539610.3934/math.2021317Study of time fractional order problems with proportional delay and controllability term via fixed point approachMuhammad Sher 0Kamal Shah1Zareen A. Khan21. Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan1. Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan2. College of Science, Mathematical Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi ArabiaIn the current manuscript, we are tying to study one of the important class of differential equations known is evolution equations. Here, we considered the problem under controllability term and with proportional delay. Before going to numerical or analytical solution it is important to check the existence and uniqueness of the solution. So, we will consider our problem for qualitative theory using fixed point theorems of Banach's and Krasnoselskii's type. For numerical solution the stability is important, hence the problem is also studied for Ulam-Hyer's type stability. At the end an example is constructed to ensure the establish results.http://www.aimspress.com/article/doi/10.3934/math.2021317?viewType=HTMLtime fractional order problems with proportional delaycontrollability termfixed point approach |
| spellingShingle | Muhammad Sher Kamal Shah Zareen A. Khan Study of time fractional order problems with proportional delay and controllability term via fixed point approach AIMS Mathematics time fractional order problems with proportional delay controllability term fixed point approach |
| title | Study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| title_full | Study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| title_fullStr | Study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| title_full_unstemmed | Study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| title_short | Study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| title_sort | study of time fractional order problems with proportional delay and controllability term via fixed point approach |
| topic | time fractional order problems with proportional delay controllability term fixed point approach |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021317?viewType=HTML |
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