A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses
In this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1<r<2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractio...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-03-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023548?viewType=HTML |
| _version_ | 1827986561024655360 |
|---|---|
| author | Marimuthu Mohan Raja Velusamy Vijayakumar Anurag Shukla Kottakkaran Sooppy Nisar Wedad Albalawi Abdel-Haleem Abdel-Aty |
| author_facet | Marimuthu Mohan Raja Velusamy Vijayakumar Anurag Shukla Kottakkaran Sooppy Nisar Wedad Albalawi Abdel-Haleem Abdel-Aty |
| author_sort | Marimuthu Mohan Raja |
| collection | DOAJ |
| description | In this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1<r<2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractional derivatives, essential conditions, mixed Volterra-Fredholm integrodifferential type, for exact controllability of the solutions are produced. Lastly, a case study is supplied to show the illustration of the primary theorems. |
| first_indexed | 2024-04-09T23:33:19Z |
| format | Article |
| id | doaj.art-bb75b1be784f4b59914ec05ee145405e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T23:33:19Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bb75b1be784f4b59914ec05ee145405e2023-03-21T01:33:17ZengAIMS PressAIMS Mathematics2473-69882023-03-0185108021082110.3934/math.2023548A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulsesMarimuthu Mohan Raja0Velusamy Vijayakumar 1Anurag Shukla2Kottakkaran Sooppy Nisar 3Wedad Albalawi 4Abdel-Haleem Abdel-Aty 51. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India2. Department of Applied Science, Rajkiya Engineering College Kannauj, Kannauj-209732, India3. Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, 16278, Saudi Arabia 4. School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India5. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia6. Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia 7. Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, EgyptIn this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1<r<2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractional derivatives, essential conditions, mixed Volterra-Fredholm integrodifferential type, for exact controllability of the solutions are produced. Lastly, a case study is supplied to show the illustration of the primary theorems.https://www.aimspress.com/article/doi/10.3934/math.2023548?viewType=HTMLfractional differential equationscontrollabilityimpulsive systemmeasure of noncompactnessvolterra-fredholm typesectorial operators |
| spellingShingle | Marimuthu Mohan Raja Velusamy Vijayakumar Anurag Shukla Kottakkaran Sooppy Nisar Wedad Albalawi Abdel-Haleem Abdel-Aty A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses AIMS Mathematics fractional differential equations controllability impulsive system measure of noncompactness volterra-fredholm type sectorial operators |
| title | A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses |
| title_full | A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses |
| title_fullStr | A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses |
| title_full_unstemmed | A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses |
| title_short | A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses |
| title_sort | new discussion concerning to exact controllability for fractional mixed volterra fredholm integrodifferential equations of order r∈ 1 2 with impulses |
| topic | fractional differential equations controllability impulsive system measure of noncompactness volterra-fredholm type sectorial operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023548?viewType=HTML |
| work_keys_str_mv | AT marimuthumohanraja anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT velusamyvijayakumar anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT anuragshukla anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT kottakkaransooppynisar anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT wedadalbalawi anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT abdelhaleemabdelaty anewdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT marimuthumohanraja newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT velusamyvijayakumar newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT anuragshukla newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT kottakkaransooppynisar newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT wedadalbalawi newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses AT abdelhaleemabdelaty newdiscussionconcerningtoexactcontrollabilityforfractionalmixedvolterrafredholmintegrodifferentialequationsoforderr12withimpulses |