Existence for a characteristic boundary value problem for an equation of mixed type in three-dimensional space

1983 ◽  
Vol 5 (1) ◽  
pp. 346-355
Author(s):  
A. H. Müller-Rettkowski ◽  
P.P. Gilbert
Keyword(s):  
Boundary Value Problem ◽  
Mixed Type ◽  
Dimensional Space ◽  
Boundary Value ◽  
Three Dimensional ◽  
Characteristic Boundary ◽  
Equation Of Mixed Type ◽  
Three Dimensional Space

A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Oleg A. Repin ◽  
Svetlana K. Kumykova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Type ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Differentiation ◽  
Uniqueness Of Solutions ◽  
Uniqueness Of The Solution ◽  
Equation Of Mixed Type

AbstractThe paper is devoted to the study of a boundary-value problem for an equation of mixed type with generalized operators of fractional differentiation in boundary conditions. We prove uniqueness of solutions under some restrictions on the known functions and on the different orders of the operators of generalized fractional differentiation appearing in the boundary conditions. Existence of solutions is proved by reduction to a Fredholm equation of the second kind, for which solvability follows from the uniqueness of the solution of our original problem.

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