On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative

doi:10.1007/s42967-023-00351-0

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (4): 1516-1539.doi: 10.1007/s42967-023-00351-0

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On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative

Dildar Ahmad¹, Amjad Ali¹, Kamal Shah^2,3, Bahaaeldin Abdalla², Thabet Abdeljawad^2,4

1. Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan;
2. Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586, Riyadh, Saudi Arabia;
3. Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan;
4. Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

收稿日期:2023-06-09 修回日期:2023-10-09 接受日期:2023-11-09 出版日期:2024-02-12 发布日期:2024-02-12
通讯作者: Thabet Abdeljawad,E-mail:tabdeljawad@psu.edu.sa E-mail:tabdeljawad@psu.edu.sa
作者简介:Dildar Ahmad, E-mail:ahmaddildar2131@gmail.com;Amjad Ali, E-mail:amjadalimna@yahoo.com;Kamal Shah, E-mail:kamalshah408@gmail.com, E-mail:kshah@psu.edu.sa;Bahaaeldin Abdalla, E-mail:babdallah@psu.edu.sa
基金资助:
Open access funding provided by Sefako Makgatho Health Sciences University.

On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative

Dildar Ahmad¹, Amjad Ali¹, Kamal Shah^2,3, Bahaaeldin Abdalla², Thabet Abdeljawad^2,4

1. Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan;
2. Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586, Riyadh, Saudi Arabia;
3. Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan;
4. Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received:2023-06-09 Revised:2023-10-09 Accepted:2023-11-09 Online:2024-02-12 Published:2024-02-12
Supported by:
Open access funding provided by Sefako Makgatho Health Sciences University.

摘要/Abstract

摘要： In this manuscript, a class of multi-term delay fractional differential equations (FDEs) under the Hilfer derivative is considered. Some newly updated results are established under boundary conditions. For the required results, we utilize the fixed point theory and tools of the nonlinear functional analysis. Further keeping in mind the importance of stability results, we develop some adequate results about the said aspect. The Hyers-Ulam (H-U)-type concept is used to derive the required stability for the solution of the considered problem. Finally, by appropriate test problems, we justify our findings.

关键词: Hilfer derivative, Multi-term, Existence results, Stability

Abstract: In this manuscript, a class of multi-term delay fractional differential equations (FDEs) under the Hilfer derivative is considered. Some newly updated results are established under boundary conditions. For the required results, we utilize the fixed point theory and tools of the nonlinear functional analysis. Further keeping in mind the importance of stability results, we develop some adequate results about the said aspect. The Hyers-Ulam (H-U)-type concept is used to derive the required stability for the solution of the considered problem. Finally, by appropriate test problems, we justify our findings.

Key words: Hilfer derivative, Multi-term, Existence results, Stability

中图分类号:

Dildar Ahmad, Amjad Ali, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad. On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1516-1539.

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On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative

On Nonlinear Analysis for Multi-term Delay Fractional Differential Equations Under Hilfer Derivative

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