TY - JOUR
T1 - An Inverse Source Non-Local Problem for a Mixed Type Equation with a Caputo Fractional Differential Operator
AU - E. Karimov, N. Al-Salti & S. Kerbal
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 417
EP - 438
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.051216.280217a
UR - https://global-sci.org/intro/article_detail/eajam/10757.html
KW - Inverse-source problem, mixed type equation, Caputo fractional operator.
AB - <p style="text-align: justify;">We 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.</p>