KASR TARTIBLI DIFFERENSIAL TENGLAMALARDA KOSHI MASALASI: BANAX FIKS NUQTA TEOREMASI ORQALI MAVJUDLIK VA YAGONALIK SHARTLARI
Keywords:
Kalit so‘zlar: kasr tartibli differensial tenglama, Koshi masalasi, Banax fiks nuqta teoremasi, qisqaruvchi tasvir, Lipschitz sharti, Volterra integral tenglama.Abstract
Annotatsiya. Mazkur maqolada kasr tartibli differensial tenglamalarda Koshi masalasi yechimining mavjudligi va yagonaligi Banax fiks nuqta teoremasi asosida asoslab beriladi. Tadqiqotning asosiy g‘oyasi shundan iboratki, kasr hosilali tenglama mos integral operator orqali Volterra tipidagi integral tenglamaga ekvivalent o‘tkaziladi va natijada yechim uzluksiz funksiyalar fazosida operatorning fiks nuqtasi sifatida talqin qilinadi. Banax fiks nuqta teoremasini qo‘llash uchun operatorning qisqaruvchi tasvir ekanini ko‘rsatish zarur bo‘lib, buning uchun o‘ng tomondagi funksiyaning Lipschitz sharti, shuningdek vaqt oraliqning uzunligi va kasr tartib parametri bilan bog‘liq baholashlar keltiriladi.
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