Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions
In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure o...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-10-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/4/252 |
| _version_ | 1797506617583861760 |
|---|---|
| author | Amadou Diop Wei-Shih Du |
| author_facet | Amadou Diop Wei-Shih Du |
| author_sort | Amadou Diop |
| collection | DOAJ |
| description | In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure of noncompactness and resolvent family theory. Under the condition that the nonlinear term is of Carathéodory type and satisfies some weakly compactness condition, we establish the existence of random mild solutions. A nontrivial example illustrating our main result is also given. |
| first_indexed | 2024-03-10T04:36:04Z |
| format | Article |
| id | doaj.art-cddfbec8830b4ffc9303bf866635e82c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:36:04Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-cddfbec8830b4ffc9303bf866635e82c2023-11-23T03:49:02ZengMDPI AGAxioms2075-16802021-10-0110425210.3390/axioms10040252Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory ConditionsAmadou Diop0Wei-Shih Du1Department of Mathematics, Université Gaston Berger de Saint-Louis, UFR SAT, Saint-Louis B.P. 234, SenegalDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanIn this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure of noncompactness and resolvent family theory. Under the condition that the nonlinear term is of Carathéodory type and satisfies some weakly compactness condition, we establish the existence of random mild solutions. A nontrivial example illustrating our main result is also given.https://www.mdpi.com/2075-1680/10/4/252measure of noncompactnessrandom effectrandom operatorMönch’s fixed point theoremmulti-term fractional differential equationCarathéodory condition |
| spellingShingle | Amadou Diop Wei-Shih Du Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions Axioms measure of noncompactness random effect random operator Mönch’s fixed point theorem multi-term fractional differential equation Carathéodory condition |
| title | Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions |
| title_full | Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions |
| title_fullStr | Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions |
| title_full_unstemmed | Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions |
| title_short | Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions |
| title_sort | existence of mild solutions for multi term time fractional random integro differential equations with random caratheodory conditions |
| topic | measure of noncompactness random effect random operator Mönch’s fixed point theorem multi-term fractional differential equation Carathéodory condition |
| url | https://www.mdpi.com/2075-1680/10/4/252 |
| work_keys_str_mv | AT amadoudiop existenceofmildsolutionsformultitermtimefractionalrandomintegrodifferentialequationswithrandomcaratheodoryconditions AT weishihdu existenceofmildsolutionsformultitermtimefractionalrandomintegrodifferentialequationswithrandomcaratheodoryconditions |