HILFER OPERATORLI KASRLI DIFFUZIYA TENGLAMASI UCHUN TESKARI MASALALAR
Keywords:
Kalit so’zlar: Rimann-Liuvill kasr integrali, Rimann-Liuvill kasr hosilasi, to’g’ri masala, teskari masala, integral tenglama, Furye qatori, mavjudlik va yagonalik, Banaxning qo’zg’almas nuqta haqidagi teoremasi.Abstract
Annotatsiya. Uhbu maqolada vaqt bo’yicha Hilfer operatorli kasrli diffuziya
tenglamasi uchun teskari masalalar ko’rib chiqiladi. To’g’ri masala bu tenglama uchun
Koshi tipidagi boshlang’ich shartlar va Drixle chegaraviy shartlar bilan berilgan
boshlang’ich-chegaraviy masaladir. Keyin, to’g’ri masalaning yechimiga qo’shimcha
shartlar qo’yish orqali tenglamadagi noma’lum koeffitsiyentlarni aniqlashning teskari
masalasini o’rganamiz. Vaqtga bog’liq koeffitsiyentni aniqlashning teskari masalasi
Volterra tipidagi ekvivalent integral tenglamaga keltiriladi. Yechimning mavjudligi va
yagonaligini isbotlash uchun qisqaruvchi akslantirishlar prinsipiga tayaniladi. Teskari
masalaning yechimining lokal mavjudligi va global yagonaligi isbotlangan. Keyin
fazoviy o’zgaruvchiga bog’liq koeffitsiyentni aniqlash bo’yicha teskari masalan
yagona yechimining mavjudligi isbotlangan.
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