Analog of the Gellerstedt problem for the mixed type equation with integral-differential operators of fractional order

2019 ◽  
Vol 2019 (3) ◽  
pp. 4-18 ◽  
Author(s):  
O.Kh Abdullaev
Keyword(s):  
Fractional Order ◽  
Mixed Type ◽  
Differential Operators ◽  
Type Equation ◽  
Mixed Type Equation ◽  
Gellerstedt Problem

scholarly journals Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
A. S. Berdyshev ◽  
E. T. Karimov ◽  
N. Akhtaeva
Keyword(s):  
Mixed Type ◽  
Differential Operators ◽  
Type Equation ◽  
Telegraph Equation ◽  
Fractional Diffusion ◽  
Tricomi Problem ◽  
Green Functions ◽  
Mixed Type Equation ◽  
Energy Integrals ◽  
Gellerstedt Problem

Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential operators have been used.

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