The Neumann problem for a mixed-type equation in a rectangular domain

2009 ◽  
Vol 53 (11) ◽  
pp. 9-15
Author(s):  
A. A. Bakhristova
Keyword(s):  
Neumann Problem ◽  
Mixed Type ◽  
Type Equation ◽  
Rectangular Domain ◽  
Mixed Type Equation ◽  
The Neumann Problem

scholarly journals An Inverse Source Non-local Problem for a Mixed Type Equation with a Caputo Fractional Differential Operator

2017 ◽  
Vol 7 (2) ◽  
pp. 417-438 ◽  
Author(s):  
E. Karimov ◽  
N. Al-Salti ◽  
S. Kerbal
Keyword(s):  
Mixed Type ◽  
Type Equation ◽  
Integral Form ◽  
Rectangular Domain ◽  
Regularity Conditions ◽  
Mixed Type Equation ◽  
Fractional Differential Operator ◽  
Non Local ◽  
Fractional Differential ◽  
The Given

AbstractWe consider the unique solvability of an inverse-source problem with integral transmitting condition for a time-fractional mixed type equation in rectangular domain where the unknown source term depends only on the space variable. The solution is based on a series expansion using a bi-orthogonal basis in space, corresponding to a non-self-adjoint boundary value problem. Under certain regularity conditions on the given data, we prove the uniqueness and existence of the solution for the given problem. The influence of the transmitting condition on the solvability of the problem is also demonstrated. Two different transmitting conditions are considered — viz. a full integral form and a special case. In order to simplify the bulky expressions appearing in the proof of our main result, we establish a new property of the recently introduced Mittag-Leffler type function in two variables.

Sign in / Sign up

Export Citation Format

Share Document