An Inverse Source Non-Local Problem for a Mixed Type Equation with a Caputo Fractional Differential Operator
Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 417–438
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.051216.280217a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 417–438
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Inverse-source problem mixed type equation Caputo fractional operator.
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