On the well-posedness of degenerate fractional differential equations in vector valued function spaces

2017 ◽  
Vol 219 (2) ◽  
pp. 727-755 ◽  
Author(s):  
Rodrigo Ponce
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Function Spaces ◽  
Well Posedness ◽  
Fractional Differential ◽  
Vector Valued Function ◽  
Vector Valued

scholarly journals On the solution of two-sided fractional ordinary differential equations of Caputo type

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Ma. Elena Hernández-Hernández ◽  
Vassili N. Kolokoltsov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Well Posedness ◽  
Solutions To Equations ◽  
Fractional Differential ◽  
The Right ◽  
Stochastic Representations ◽  
Exit Problems ◽  
Special Case

AbstractThis paper provides well-posedness results and stochastic representations for the solutions to equations involving both the right- and the left-sided generalized operators of Caputo type. As a special case, these results show the interplay between two-sided fractional differential equations and two-sided exit problems for certain Lévy processes.

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