On the solvability of the first boundary value problem for the loaded equation of heat conduction - Jenaliyev, M.T.; Iskakov, S.A.; Ramazanov, M.I.; Tuleutaeva, Zh.M. (KSU Publ., 2018)
In this paper we consider the first boundary value problem for the loaded equation of heat conduction in a quarter plane. The loaded term is the trace of the fractional derivative of order ν, 0 ≤ ν ≤ 1 with respect to the time variable on the line x = t. It is shown that when 0 ≤ ν ≤ 1 and ∀λ ∈C, then the load is a weak perturbation, that is, the studied problem has a unique solution in the class of bounded functions.
Жүктелген жылуөткiзгiштiк теңдеуi yшiн бiрiншi шеттiк есептiң шешiмдiлiгi туралы
О разрешимости первой краевой задачи для нагруженного уравнения теплопроводности
Keywords: loaded equation of heat conduction; boundary value problem; fractional derivative; Volterra integral equation