Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order
In this research paper, we study a coupled system of piecewise-order differential equations (DEs) with variable kernel and impulsive conditions. DEs with variable kernel have high flexibility due to the freedom of changing the kernel. We study existence and stability theory and derive sufficient con...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/6/436 |
| _version_ | 1827737362194497536 |
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| author | Arshad Ali Khursheed J. Ansari Hussam Alrabaiah Ahmad Aloqaily Nabil Mlaiki |
| author_facet | Arshad Ali Khursheed J. Ansari Hussam Alrabaiah Ahmad Aloqaily Nabil Mlaiki |
| author_sort | Arshad Ali |
| collection | DOAJ |
| description | In this research paper, we study a coupled system of piecewise-order differential equations (DEs) with variable kernel and impulsive conditions. DEs with variable kernel have high flexibility due to the freedom of changing the kernel. We study existence and stability theory and derive sufficient conditions for main results of the proposed problem. We apply Scheafer’s fixed point theorem and Banach fixed point theorem for the result of at least one and unique solution, respectively. In addition, stability results based on the Ulam–Hyers concept are derived. Being a coupled system of piecewise fractional-order DEs with variable kernel and impulsive effects, the obtained results have multi-dimension applications. To demonstrate the applications, we apply the derived results to a numerical problem. |
| first_indexed | 2024-03-11T02:27:47Z |
| format | Article |
| id | doaj.art-9663e836eaee4108bab0f82b2ababd66 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T02:27:47Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9663e836eaee4108bab0f82b2ababd662023-11-18T10:29:17ZengMDPI AGFractal and Fractional2504-31102023-05-017643610.3390/fractalfract7060436Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise OrderArshad Ali0Khursheed J. Ansari1Hussam Alrabaiah2Ahmad Aloqaily3Nabil Mlaiki4Department of Mathematics, University of Malakand, Chakdara Dir (L), Chakdara P.O. Box 18800, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaCollege of Engineering, Al Ain University, Al Ain P.O. Box 64141, United Arab EmiratesDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaIn this research paper, we study a coupled system of piecewise-order differential equations (DEs) with variable kernel and impulsive conditions. DEs with variable kernel have high flexibility due to the freedom of changing the kernel. We study existence and stability theory and derive sufficient conditions for main results of the proposed problem. We apply Scheafer’s fixed point theorem and Banach fixed point theorem for the result of at least one and unique solution, respectively. In addition, stability results based on the Ulam–Hyers concept are derived. Being a coupled system of piecewise fractional-order DEs with variable kernel and impulsive effects, the obtained results have multi-dimension applications. To demonstrate the applications, we apply the derived results to a numerical problem.https://www.mdpi.com/2504-3110/7/6/436fractional piecewise order derivativevariable kernelexistence of solutionstability results |
| spellingShingle | Arshad Ali Khursheed J. Ansari Hussam Alrabaiah Ahmad Aloqaily Nabil Mlaiki Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order Fractal and Fractional fractional piecewise order derivative variable kernel existence of solution stability results |
| title | Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order |
| title_full | Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order |
| title_fullStr | Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order |
| title_full_unstemmed | Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order |
| title_short | Coupled System of Fractional Impulsive Problem Involving Power-Law Kernel with Piecewise Order |
| title_sort | coupled system of fractional impulsive problem involving power law kernel with piecewise order |
| topic | fractional piecewise order derivative variable kernel existence of solution stability results |
| url | https://www.mdpi.com/2504-3110/7/6/436 |
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