KASR TARTIBLI UMUMLASHGAN RIMAN LIUVILL DIFFERENSIAL OPERATORLI TENGLAMA UCHUN TESKARI MASALA
Keywords:
Hilfer kasr hosilasi, boshlang‘ich chegaravir shart, Koshi masalasi, integral tenglama, mavjudlik, yagona , tekis yaqinlashuvchi qator.Abstract
Ushbu maqolada boshlang‘ich-nolokal chegaraviy shartli vaqt kasr to‘lqin tenglamasi uchun teskari masala o‘rganildi. Biz boshlang‘ich-nolokal chegaraviy shartli masalani tadqiq etishda, dastlab fazo o‘zgaruvchisiga bog‘liq spektral masala o‘rganildi. Spektral masalaning xos soni va xos funksiyalari aniqlandi. Vaqt o‘zgaruvchisi bo‘yicha Koshi masalasi olindi. Bu Koshi masalasi ekvivalent bo‘lgan integral tenglama olindi. Integral tenglamaning yechimi mavjudligi va yagonaligi isbotlandi. So‘ngra boshlang‘ich chegaraviy masala yechimi qator ko‘rinishda izlaymiz. Qatorning tekis darajada uzluksizligi isbotlaymiz. Shundan so‘ng kasr tartibli umumlashgan Riman Liuvill differensial operatorli tenglama uchun teskari masala” tadqiq etamiz, unda to‘g‘ri masala yechimiga qo‘shimcha shart berish orqali tenglamada qatnashuvchi nomalum koeffitsiyentni aniqlash masalasi o‘rganamiz. Bunda asosan teskari masala unga ekvivalent integral tenglamaga keltiramiz, so‘ngra siqiluvchan akslantirishlar prinsipi yordamida teskari masalaning yechimi mavjudligi va yagonaligi isbotlaymiz.
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