Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative
In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some exa...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/13/1479 |
| _version_ | 1827688876402016256 |
|---|---|
| author | Jorge Sanchez-Ortiz Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Martin P. Arciga-Alejandre |
| author_facet | Jorge Sanchez-Ortiz Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Martin P. Arciga-Alejandre |
| author_sort | Jorge Sanchez-Ortiz |
| collection | DOAJ |
| description | In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given. |
| first_indexed | 2024-03-10T10:06:48Z |
| format | Article |
| id | doaj.art-b41d03ce24d04b56b462de890bfd230d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:06:48Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b41d03ce24d04b56b462de890bfd230d2023-11-22T01:31:51ZengMDPI AGMathematics2227-73902021-06-01913147910.3390/math9131479Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô DerivativeJorge Sanchez-Ortiz0Omar U. Lopez-Cresencio1Francisco J. Ariza-Hernandez2Martin P. Arciga-Alejandre3Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, MexicoFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, MexicoFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, MexicoFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, MexicoIn this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.https://www.mdpi.com/2227-7390/9/13/1479brownian motionCaputo-Itô derivativeItô processexistenceuniqueness |
| spellingShingle | Jorge Sanchez-Ortiz Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Martin P. Arciga-Alejandre Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative Mathematics brownian motion Caputo-Itô derivative Itô process existence uniqueness |
| title | Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative |
| title_full | Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative |
| title_fullStr | Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative |
| title_full_unstemmed | Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative |
| title_short | Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative |
| title_sort | cauchy problem for a stochastic fractional differential equation with caputo ito derivative |
| topic | brownian motion Caputo-Itô derivative Itô process existence uniqueness |
| url | https://www.mdpi.com/2227-7390/9/13/1479 |
| work_keys_str_mv | AT jorgesanchezortiz cauchyproblemforastochasticfractionaldifferentialequationwithcaputoitoderivative AT omarulopezcresencio cauchyproblemforastochasticfractionaldifferentialequationwithcaputoitoderivative AT franciscojarizahernandez cauchyproblemforastochasticfractionaldifferentialequationwithcaputoitoderivative AT martinparcigaalejandre cauchyproblemforastochasticfractionaldifferentialequationwithcaputoitoderivative |