On the Cauchy problems for Barenblatt-Zheltov-Kochina type fractional equations
В данной статье исследуется задача Коши для однородного дробного уравнения типа
Баренблатта-Жельтова-Кочина с производной Капуто. Существование решения поставленной
задачи Коши показано с использованием метода Фурье, а непрерывность найденного решения
доказывается на основе свойств функциональных рядов. Кроме того, устанавливается един-
ственность решения. В процессе доказательства существования и единственности решения за-
дачи широко используются свойства функции Миттага-Лефлера.
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