«FarDU ilmiy xabarlari» Volume 31 Issue 6 (2025)
TO‘G‘RI TO‘RTBURCHAKLI SOHADA BUZILADIGAN SUBDIFFUZIYA TENGLAMASI UCHUN ARALASH CHEGARAVIY MASALANING YECHILISHI
Ikramova, Nargis, Yunusalieva, Mokhinur
Abstract
<p><em>Ushbu maqolada to‘g‘ri to‘rtburchak sohada buziladigan subdiffuziya tenglamasi uchun aralash chegaraviy masala o‘rganilgan. O‘zgaruvchilarni ajratish usuli yordamida fazoviy o‘zgaruvchiga bog‘liq bo‘lgan oddiy differensial tenglama uchun spektral masala hosil qilinadi. Hosil bo‘lgan spektral masalaning xos qiymatlari va xos funksiyalarining mavjudligi musbat differensial operatorlar nazariyasiga asoslanib isbotlangan. Masalaning yechimi Furye qatori ko‘rinishida qurilgan. Olingan qatorning yaqinlashuvchiligi isbotlangan hamda yechimning yagonaligi xos funksiyalar sistemasining to‘laligidan foydalanib asoslangan.</em></p>
kasr tartibli hisobbuziladigandifferensial tenglamaaralash masalakasr tartibli Kaputo differensial operatorispektral masala.fractional calculusdegenerate differential equationmixed problemCaputo fractional differential operatorspectral problem.
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