Determination of the kernel for a time fractional diffusion equation with integral type over-determining conditions Amrilloyeva Kibriyo Sadridinovna

Determination of the kernel for a time fractional diffusion equation with integral type over-determining conditions
Amrilloyeva Kibriyo Sadridinovna
Master student of Bukhara State University, Bukhara, Uzbekistan
E_mail: [e-mail]

Let be fixed number and .

Consider the inverse problem of determining of functions such that it satisfies the equation
(1)

with initial and nonlocal boundary conditions
(2)
(3)
and the additional condition
(4)
Where is the Caputo fractional derivative [1]-[3] of order in the time variable, difined by

and are given functions of and .
Theorem. Let and be satisfied. Then the inverse problem has a unique solution for some small . Then there exists sufficiently small number that the solution to the problem in the class of functions exsist and unique , where .
REFERENCES
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3. D. G. Gordeziani, G. A. Avalishvili, On the constructing of solutions of the nonlocal initial boundary value problems for one-dimensional medium oscillation equations (in Russian), Mat. Model. 12(2000), No. 1, 94 -103.