DOIRAVIY SOHADA FAZO-VAQT KASR TARTIBLI SUPERDIFFUZIYA TENGLAMASINING ANALITIK YECHILUVCHANLIGI VA SPEKTRAL XOSSALARI
Keywords:
superdiffuziya, Kaputo hosilasi, spektral kasrli Laplas operatori, doiraviy soha, Furye-Bessel qatori, Mittag-Leffler funksiyasi, mavjudlik va yagonalik, Alikaxanov-Andreev tengsizligi.Abstract
Ushbu maqolada bir jinsli Dirixle chegaraviy shartlari ostida ikki o‘lchamli tekis doiraviy sohada fazo va vaqt bo‘yicha kasr tartibli superdiffuziya tenglamasi uchun qo‘yilgan boshlang‘ich-chegaraviy masala tadqiq etilgan. Vaqt bo‘yicha jarayon evolyutsiyasi tartibli Kaputo kasrli hosilasi orqali, zarrachalarning uzoq masofalarga sakrashini (Levi parvozlarini) ifodalovchi fazoviy nolokallik esa qutb koordinatalaridagi tartibli spektral kasrli Laplas operatori orqali modellashtirilgan. Shturm-Liuvill spektral nazariyasini qo‘llash orqali masalaning aniq analitik yechimi ikki parametrli Mittag-Leffler funksiyalarini o‘z ichiga olgan ikki karrali cheksiz Furye-Bessel qatori ko‘rinishida qurilgan. Yechimning mavjudligi va tekis yaqinlashishi Sobolev fazolarida Veyershtrass alomati yordamida, yagonaligi esa Alikaxanov-Andreev kasrli differensial tengsizligiga asoslangan energetik integrallar metodi orqali qat’iy isbotlangan. Kasr tartibli parametrlarning anomal ko‘chish jadalligiga ko‘rsatadigan jismoniy ta’siri muhokama qilingan.
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