Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay
This study establishes the existence and stability of solutions for a general class of Riemann–Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay. Our findings are confirmed by the fixed-point theorems (FPTs) from the available literature. We transform the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/339 |
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| author | Benoumran Telli Mohammed Said Souid Jehad Alzabut Hasib Khan |
| author_facet | Benoumran Telli Mohammed Said Souid Jehad Alzabut Hasib Khan |
| author_sort | Benoumran Telli |
| collection | DOAJ |
| description | This study establishes the existence and stability of solutions for a general class of Riemann–Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay. Our findings are confirmed by the fixed-point theorems (FPTs) from the available literature. We transform the RL FDE of variable order to alternate RL fractional integral structure, then with the use of classical FPTs, the existence results are studied and the Hyers–Ulam stability is established by the help of standard notions. The approach is more broad-based and the same methodology can be used for a number of additional issues. |
| first_indexed | 2024-03-11T05:15:26Z |
| format | Article |
| id | doaj.art-d21889efe9da49d3a937069a0c494638 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:15:26Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-d21889efe9da49d3a937069a0c4946382023-11-17T18:19:01ZengMDPI AGAxioms2075-16802023-03-0112433910.3390/axioms12040339Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with DelayBenoumran Telli0Mohammed Said Souid1Jehad Alzabut2Hasib Khan3Department of Mathematics, University of Tiaret, Tiaret 14035, AlgeriaDepartment of Economic Sciences, University of Tiaret, Tiaret 14035, AlgeriaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThis study establishes the existence and stability of solutions for a general class of Riemann–Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay. Our findings are confirmed by the fixed-point theorems (FPTs) from the available literature. We transform the RL FDE of variable order to alternate RL fractional integral structure, then with the use of classical FPTs, the existence results are studied and the Hyers–Ulam stability is established by the help of standard notions. The approach is more broad-based and the same methodology can be used for a number of additional issues.https://www.mdpi.com/2075-1680/12/4/339fractional differential equations of variable orderfixed-point theoremsexistence of solutionsHyers–Ulam stability |
| spellingShingle | Benoumran Telli Mohammed Said Souid Jehad Alzabut Hasib Khan Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay Axioms fractional differential equations of variable order fixed-point theorems existence of solutions Hyers–Ulam stability |
| title | Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay |
| title_full | Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay |
| title_fullStr | Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay |
| title_full_unstemmed | Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay |
| title_short | Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay |
| title_sort | existence and uniqueness theorems for a variable order fractional differential equation with delay |
| topic | fractional differential equations of variable order fixed-point theorems existence of solutions Hyers–Ulam stability |
| url | https://www.mdpi.com/2075-1680/12/4/339 |
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