Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system
Abstract The primary focus of this paper is to explore the concept of an initial condition for a noninstantaneous impulsive fractional integro-differential equation of order 0 < ϑ < 1 $0<\vartheta <1$ in an n-dimensional Euclidean space. Using the Laplace transform method, we derive the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
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| Online Access: | https://doi.org/10.1186/s13663-024-00778-x |
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| author | Kanagaraj Muthuselvan Baskar Sundaravadivoo Shankar Rao Munjam Kottakkaran Sooppy Nisar |
| author_facet | Kanagaraj Muthuselvan Baskar Sundaravadivoo Shankar Rao Munjam Kottakkaran Sooppy Nisar |
| author_sort | Kanagaraj Muthuselvan |
| collection | DOAJ |
| description | Abstract The primary focus of this paper is to explore the concept of an initial condition for a noninstantaneous impulsive fractional integro-differential equation of order 0 < ϑ < 1 $0<\vartheta <1$ in an n-dimensional Euclidean space. Using the Laplace transform method, we derive the solution representation of the given dynamical system and investigate the existence and uniqueness of the mild solution through the topological degree method and Gronwall’s inequality. Furthermore, we present a filter model featuring a finite impulsive response, which serves as a practical demonstration of the proposed system because it effectively captures the memory effects inherent in fractional-order systems and enhances system reliability with minimal input. Finally, the numerical computations with graphical illustrations provide concrete examples that validate the theoretical results, showcasing how the behavior of the system is impacted by changes in fractional order and emphasizing the versatility of our proposed method. |
| format | Article |
| id | doaj-art-c4fc2e02fd624a27944be77243d24ac3 |
| institution | Kabale University |
| issn | 2730-5422 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj-art-c4fc2e02fd624a27944be77243d24ac32025-01-19T12:36:20ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222025-01-012025111510.1186/s13663-024-00778-xNovel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering systemKanagaraj Muthuselvan0Baskar Sundaravadivoo1Shankar Rao Munjam2Kottakkaran Sooppy Nisar3Department of Mathematics, Alagappa UniversityDepartment of Mathematics, Central University of Tamil NaduSchool of Technology, Woxsen UniversityDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz UniversityAbstract The primary focus of this paper is to explore the concept of an initial condition for a noninstantaneous impulsive fractional integro-differential equation of order 0 < ϑ < 1 $0<\vartheta <1$ in an n-dimensional Euclidean space. Using the Laplace transform method, we derive the solution representation of the given dynamical system and investigate the existence and uniqueness of the mild solution through the topological degree method and Gronwall’s inequality. Furthermore, we present a filter model featuring a finite impulsive response, which serves as a practical demonstration of the proposed system because it effectively captures the memory effects inherent in fractional-order systems and enhances system reliability with minimal input. Finally, the numerical computations with graphical illustrations provide concrete examples that validate the theoretical results, showcasing how the behavior of the system is impacted by changes in fractional order and emphasizing the versatility of our proposed method.https://doi.org/10.1186/s13663-024-00778-xFractional differential equationMild solutionNoninstantaneous impulseTopological degree methodGronwall’s inequality |
| spellingShingle | Kanagaraj Muthuselvan Baskar Sundaravadivoo Shankar Rao Munjam Kottakkaran Sooppy Nisar Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system Fixed Point Theory and Algorithms for Sciences and Engineering Fractional differential equation Mild solution Noninstantaneous impulse Topological degree method Gronwall’s inequality |
| title | Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system |
| title_full | Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system |
| title_fullStr | Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system |
| title_full_unstemmed | Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system |
| title_short | Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system |
| title_sort | novel exploration of topological degree method for noninstantaneous impulsive fractional integro differential equation through the application of filtering system |
| topic | Fractional differential equation Mild solution Noninstantaneous impulse Topological degree method Gronwall’s inequality |
| url | https://doi.org/10.1186/s13663-024-00778-x |
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