КЛАСИЧНИЙ РОЗВ'ЯЗОК ОБЕРНЕНО1 ЗАДАЧ1 Д Л Я Р1ВНЯННЯ ДРОБОВО1 ДИФУЗП ПРИ 1НТЕГРАЛЬН1Й ЗА ЧАСОМ УМОВ1 ПЕРЕВИЗНАЧЕННЯ (Russian)

We prove the correctness of the inverse problem on determination of a~pare of functions: a~classical solution u of the first boundary value problem for linear diffusion equation Dαtu-uxx=F0(x),(x,t)∈(0,l)×(0,T] with regularized fractional derivative of order α∈(0,1) with respect to time and function F0(x) under integral by time over-determination condition. Доказана корректность обратной задачи об определении пары функций: классическо- го решения u первой краевой задачи для линейного уравнения диффузии Dfu -- uxx = Fo(x), (x,t) G (0, l) x (0, T] с регуляризованной дробной производной порядка a G (0,1) по времени и функции Fo(x) при интегральном по времени условии переопределения. [ABSTRACT FROM AUTHOR]

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