Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators
This work is devoted to the analysis of Hyers, Ulam, and Rassias types of stabilities for nonlinear fractional integral equations with $ n $-product operators. In some special cases, our considered integral equation is related to an integral equation which arises in the study of the spread of an inf...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024377?viewType=HTML |
| _version_ | 1797277580236161024 |
|---|---|
| author | Supriya Kumar Paul Lakshmi Narayan Mishra |
| author_facet | Supriya Kumar Paul Lakshmi Narayan Mishra |
| author_sort | Supriya Kumar Paul |
| collection | DOAJ |
| description | This work is devoted to the analysis of Hyers, Ulam, and Rassias types of stabilities for nonlinear fractional integral equations with $ n $-product operators. In some special cases, our considered integral equation is related to an integral equation which arises in the study of the spread of an infectious disease that does not induce permanent immunity. $ n $-product operators are described here in the sense of Riemann-Liouville fractional integrals of order $ \sigma_i \in (0, 1] $ for $ i\in \{1, 2, \dots, n\} $. Sufficient conditions are provided to ensure Hyers-Ulam, $ \lambda $-semi-Hyers-Ulam, and Hyers-Ulam-Rassias stabilities in the space of continuous real-valued functions defined on the interval $ [0, a] $, where $ 0 < a < \infty $. Those conditions are established by applying the concept of fixed-point arguments within the framework of the Bielecki metric and its generalizations. Two examples are discussed to illustrate the established results. |
| first_indexed | 2024-03-07T15:51:29Z |
| format | Article |
| id | doaj.art-87a4c78131bb4a339f5d94519d55d442 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T15:51:29Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-87a4c78131bb4a339f5d94519d55d4422024-03-05T01:18:34ZengAIMS PressAIMS Mathematics2473-69882024-02-01947770779010.3934/math.2024377Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operatorsSupriya Kumar Paul0Lakshmi Narayan Mishra1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaThis work is devoted to the analysis of Hyers, Ulam, and Rassias types of stabilities for nonlinear fractional integral equations with $ n $-product operators. In some special cases, our considered integral equation is related to an integral equation which arises in the study of the spread of an infectious disease that does not induce permanent immunity. $ n $-product operators are described here in the sense of Riemann-Liouville fractional integrals of order $ \sigma_i \in (0, 1] $ for $ i\in \{1, 2, \dots, n\} $. Sufficient conditions are provided to ensure Hyers-Ulam, $ \lambda $-semi-Hyers-Ulam, and Hyers-Ulam-Rassias stabilities in the space of continuous real-valued functions defined on the interval $ [0, a] $, where $ 0 < a < \infty $. Those conditions are established by applying the concept of fixed-point arguments within the framework of the Bielecki metric and its generalizations. Two examples are discussed to illustrate the established results.https://www.aimspress.com/article/doi/10.3934/math.2024377?viewType=HTMLhyers-ulam stability$ \lambda $-semi-hyers-ulam stabilityhyers-ulam-rassias stabilityfractional integral equationbielecki metric |
| spellingShingle | Supriya Kumar Paul Lakshmi Narayan Mishra Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators AIMS Mathematics hyers-ulam stability $ \lambda $-semi-hyers-ulam stability hyers-ulam-rassias stability fractional integral equation bielecki metric |
| title | Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators |
| title_full | Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators |
| title_fullStr | Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators |
| title_full_unstemmed | Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators |
| title_short | Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators |
| title_sort | stability analysis through the bielecki metric to nonlinear fractional integral equations of n product operators |
| topic | hyers-ulam stability $ \lambda $-semi-hyers-ulam stability hyers-ulam-rassias stability fractional integral equation bielecki metric |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024377?viewType=HTML |
| work_keys_str_mv | AT supriyakumarpaul stabilityanalysisthroughthebieleckimetrictononlinearfractionalintegralequationsofnproductoperators AT lakshminarayanmishra stabilityanalysisthroughthebieleckimetrictononlinearfractionalintegralequationsofnproductoperators |