Mathematics
(Jun 2021)
Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative
Jorge Sanchez-Ortiz,
Omar U. Lopez-Cresencio,
Francisco J. Ariza-Hernandez,
Martin P. Arciga-Alejandre
Affiliations
Jorge Sanchez-Ortiz
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
Omar U. Lopez-Cresencio
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
Francisco J. Ariza-Hernandez
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
Martin P. Arciga-Alejandre
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
DOI
https://doi.org/10.3390/math9131479
Journal volume & issue
Vol. 9,
no. 13
Abstract
Read online
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.
Keywords
WeChat QR code
Close
