stochastic fractional differential equation
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scholarly journals Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1479
Author(s):  
Jorge Sanchez-Ortiz ◽  
Omar U. Lopez-Cresencio ◽  
Francisco J. Ariza-Hernandez ◽  
Martin P. Arciga-Alejandre
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Stochastic Fractional Differential Equation ◽  
Fractional Differential

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.

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