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Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time. (English) Zbl 1231.35289
Summary: We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.
MSC:
35R11Fractional partial differential equations
35K05Heat equation
35R30Inverse problems for PDE
26A33Fractional derivatives and integrals (real functions)
45K05Integro-partial differential equations
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