Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques
Abstract This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable b...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-11-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01957-w |
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| author | Doha A. Kattan Hasanen A. Hammad |
| author_facet | Doha A. Kattan Hasanen A. Hammad |
| author_sort | Doha A. Kattan |
| collection | DOAJ |
| description | Abstract This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable boundary conditions. To account for abrupt state changes, impulsive conditions are integrated into the model. The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. The practical applicability of our findings is demonstrated through an illustrative example. |
| format | Article |
| id | doaj-art-802583d0f35a443693a15c26fd6d070f |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-802583d0f35a443693a15c26fd6d070f2024-11-10T12:35:17ZengSpringerOpenBoundary Value Problems1687-27702024-11-012024112010.1186/s13661-024-01957-wSolving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniquesDoha A. Kattan0Hasanen A. Hammad1Department of Mathematics, College of Sciences and Art, King Abdulaziz UniversityDepartment of Mathematics, College of Science, Qassim UniversityAbstract This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable boundary conditions. To account for abrupt state changes, impulsive conditions are integrated into the model. The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. The practical applicability of our findings is demonstrated through an illustrative example.https://doi.org/10.1186/s13661-024-01957-wDifferential equationsRelaxation impulsive termsFractional derivativesExistence resultsFixed point techniquesEvolution metrics |
| spellingShingle | Doha A. Kattan Hasanen A. Hammad Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques Boundary Value Problems Differential equations Relaxation impulsive terms Fractional derivatives Existence results Fixed point techniques Evolution metrics |
| title | Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques |
| title_full | Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques |
| title_fullStr | Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques |
| title_full_unstemmed | Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques |
| title_short | Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques |
| title_sort | solving fractional integro differential equations with delay and relaxation impulsive terms by fixed point techniques |
| topic | Differential equations Relaxation impulsive terms Fractional derivatives Existence results Fixed point techniques Evolution metrics |
| url | https://doi.org/10.1186/s13661-024-01957-w |
| work_keys_str_mv | AT dohaakattan solvingfractionalintegrodifferentialequationswithdelayandrelaxationimpulsivetermsbyfixedpointtechniques AT hasanenahammad solvingfractionalintegrodifferentialequationswithdelayandrelaxationimpulsivetermsbyfixedpointtechniques |