DOIRADA BERILGAN KASR TARTIBLI SUBDIFFUZIYA TENGLAMASI UCHUN BOSHLANG'ICH CHEGARAVIY MASALANI YECHISH
Keywords:
Kalit so‘zlar: kasr tartibli differensial tenglama, subdiffuziya, boshlang‘ich- chegaraviy masala, analitik yechim, numerik usul, doira, fizik jarayon, xotira effekti, Fraktsional hisoblash, anomal diffuziya.Abstract
Annotatsiya: Ushbu ilmiy ishda doirada berilgan kasr tartibli subdiffuziya
tenglamasi uchun boshlang‘ich-chegaraviy masalani yechish masalasi batafsil ko‘rib
chiqiladi. Kasr tartibli subdiffuziya tenglamalari orqali fizik jarayonlarning klassik
modellenishidan farqli o‘laroq, murakkab, masalan, xotira effektiga ega yoki
inertsiyali fizik tizimlarni tavsiflash mumkinligi asoslanadi. Ishda aynan doiraviy
sohada subdiffuziya tenglamasi uchun boshlang‘ich va chegaraviy shartlar bilan
qo‘shimcha masala tuziladi, umumiy yechimni topish uchun analitik va numerik
usullar ko‘rib chiqiladi, mutaxassis va talabalarga tushunarli tarzda ilmiy izohlar
keltiriladi. Olingan natijalarning matematik jixatlari, fizik ma’nosi va amaliy
qo‘llanilishi, shuningdek, kasr tartibli hisoblashlarning zamonaviy muhandislik va
fizika sohalarida o‘rni mufassal tahlil qilinadi. Mazkur tadqiqot kasr tartibli darajali
hodisalarning tahliliga bag‘ishlangan, zamonaviy ilmiy tadqiqotlarda
foydalanilayotgan yechim metodikalarining afzalliklarini yoritadi.
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