Теорема существования и единственности слабого решения дробной параболической задачи методом Роте
https://doi.org/10.17586/2220-8054-2024-15-1-5-15
Аннотация
Целью данной работы является исследование существования и единственности слабого решения краевой задачи дробного уравнения по времени, включающего дробную производную Капуто с интегральным оператором. Используя метод дискретизации, мы сначала получаем некоторые априорные оценки приближенных решений в точках (x, tj). Затем мы оценим точность предложенного метода, чтобы продемонстрировать, что реализованная последовательность α-функций Роте сходится в определенном смысле, а ее предел является решением (в слабом смысле) нашей задачи. Следует отметить, что построенная схема L1 предназначена для аппроксимации упомянутой в задаче дробной производной Капуто.
Об авторах
Ю. Бекакра
ICOSI Laboratory, Abbes Laghrour University
Алжир
Алжир
А. Бузиани
ICOSI Laboratory, Abbes Laghrour University; L’arbi Ben M’hidi University
Алжир
Алжир
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Рецензия
Для цитирования:
Бекакра Ю., Бузиани А. Теорема существования и единственности слабого решения дробной параболической задачи методом Роте. Наносистемы: физика, химия, математика. 2024;15(1):5-15. https://doi.org/10.17586/2220-8054-2024-15-1-5-15
For citation:
Bekakra Y., Bouziani A. Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(1):5-15. https://doi.org/10.17586/2220-8054-2024-15-1-5-15
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