Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations
Abstract In this paper we consider impulsive delay differential equations with the Caputo fractional derivative with respect to another function on a finite interval. We set up and study a problem that consists of an initial condition on the initial time interval and a nonlinear boundary condition....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-04-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02045-3 |
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| author | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_facet | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | Abstract In this paper we consider impulsive delay differential equations with the Caputo fractional derivative with respect to another function on a finite interval. We set up and study a problem that consists of an initial condition on the initial time interval and a nonlinear boundary condition. This mixed boundary value problem depends on a parameter. We obtain an integral presentation of the solution and establish the existence and uniqueness of the solution for any value of the real valued parameter. We discuss the Ulam type stability for boundary value problems and, based on the application of an appropriate modification of the classical definition, we suggest a way to study this type of stability. We keep the idea that the solution of the studied problem will depend significantly on the chosen solution of the corresponding differential inequality, and this is based on an appropriate choice of the parameter involved in the boundary condition. Some examples are given to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-e2fe3351fa4a418f8cfa2ea8cb2c5a03 |
| institution | DOAJ |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-e2fe3351fa4a418f8cfa2ea8cb2c5a032025-08-20T03:07:43ZengSpringerOpenBoundary Value Problems1687-27702025-04-012025112010.1186/s13661-025-02045-3Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equationsRavi P. Agarwal0Snezhana Hristova1Donal O’Regan2Department of Mathematics and Systems Engineering, Florida Institute of TechnologyFaculty of Mathematics and Informatics, Plovdiv UniversitySchool of Mathematical and Statistical Sciences, University of GalwayAbstract In this paper we consider impulsive delay differential equations with the Caputo fractional derivative with respect to another function on a finite interval. We set up and study a problem that consists of an initial condition on the initial time interval and a nonlinear boundary condition. This mixed boundary value problem depends on a parameter. We obtain an integral presentation of the solution and establish the existence and uniqueness of the solution for any value of the real valued parameter. We discuss the Ulam type stability for boundary value problems and, based on the application of an appropriate modification of the classical definition, we suggest a way to study this type of stability. We keep the idea that the solution of the studied problem will depend significantly on the chosen solution of the corresponding differential inequality, and this is based on an appropriate choice of the parameter involved in the boundary condition. Some examples are given to illustrate the theoretical results.https://doi.org/10.1186/s13661-025-02045-3Caputo type fractional derivative with respect to another functionFractional differential equationDelayImpulsesBoundary value problemUlam type stability |
| spellingShingle | Ravi P. Agarwal Snezhana Hristova Donal O’Regan Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations Boundary Value Problems Caputo type fractional derivative with respect to another function Fractional differential equation Delay Impulses Boundary value problem Ulam type stability |
| title | Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations |
| title_full | Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations |
| title_fullStr | Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations |
| title_full_unstemmed | Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations |
| title_short | Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations |
| title_sort | ulam stability for nonlinear boundary value problems for impulsive caputo type fractional delay differential equations |
| topic | Caputo type fractional derivative with respect to another function Fractional differential equation Delay Impulses Boundary value problem Ulam type stability |
| url | https://doi.org/10.1186/s13661-025-02045-3 |
| work_keys_str_mv | AT ravipagarwal ulamstabilityfornonlinearboundaryvalueproblemsforimpulsivecaputotypefractionaldelaydifferentialequations AT snezhanahristova ulamstabilityfornonlinearboundaryvalueproblemsforimpulsivecaputotypefractionaldelaydifferentialequations AT donaloregan ulamstabilityfornonlinearboundaryvalueproblemsforimpulsivecaputotypefractionaldelaydifferentialequations |