THE CAUCHY PROBLEM FOR A HIGH-ORDER ORDINARY DIFFERENTIAL EQUATION INVOLVING THE BESSEL OPERATOR AND LOWER-ORDER TERMS
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Ushbu maqolada spektral parametrga ega bo‘lgan Bessel operatori ishtirok etgan yuqori tartibli
oddiy differensial tenglama uchun Koshi masalasi tadqiq qilinadi. Bunday turdagi masalalar sezilarli
murakkabliklarga ega bo‘lib, mos analitik vositalarning yetishmasligi sababli ilmiy adabiyotlarda kam
o‘rganilgan. Tadqiqotning asosiy maqsadi - almashtirish operatoridan foydalanib, Koshi masalasining
yechimini olishdir. Almashtirish operatori sifatida umumlashtirilgan Erdelyi-Kober kasr operatori
qo‘llaniladi. Bu operator qo‘llanganda, ko‘rib chiqilayotgan masala singulyar koefisentsiz va pastroq
tartibli hadi bo‘lmagan tenglamaga keltiriladi. Taklif etilgan yondashuvning muhim afzalliklaridan
biri shundaki, u qo‘yilgan masalaning aniq yechimini olishga imkon beradi. Zamonaviy hisoblash
texnologiyalarida katta yutuqlarga erishilganiga qaramay, oddiy differensial tenglamalarning chegara
masalalari uchun aniq yechimlarni topish hanuz muhim va dolzarb masala bo‘lib qolmoqda. Bunday
yechimlar tasvirlanayotgan jarayon va hodisalarning sifat jihatdan xatti-harakatini chuqurroq
anglashga, asosiy matematik modellarning ichki xususiyatlarini ochib berishga hamda asimptotik
va sonli metodlar uchun tayanch misollar sifatida xizmat qilishga yordam beradi.
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