Kasr tartibli diffuziya tenglamasi fundamental yechimi mavzusida bajarilgan magistrlik dissertatsiyasi

O’ZBEKISTON RESPUBLIKASI OLIY VA O’RTA MAXSUS TA’LIM VAZIRLIGI
ABDULLA QODIRIY NOMIDAGI JIZZAX DAVLAT PEDAGOGIKA INSTITUTI
MAGISTRATURA BO’LIMI
UDK: 371.3
BURXONOV MA'SUDJON DAMIR O’G’LINING
KASR TARTIBLI DIFFUZIYA TENGLAMASI FUNDAMENTAL YECHIMI

MAVZUSIDA BAJARILGAN

MAGISTRLIK DISSERTATSIYASI

5A110101 – Aniq va tabiiy fanlar o`qitish metodikasi (Matematika)

“Matematika o’qitish metodikasi” kafedrasi yig’ilishining qarori bilan
(Qaror №_______) himoyaga tavsiya etilgan
“Himoyaga tavsiya qilindi”
_______ p.f.d., prof. R.Yarmatov
“___” “______________” 2022 yil

Kafedra mudiri: _________ p.f.n.dots.J.B.Ergashev

Ishni himoyaga tavsiya etaman.

Ilmiy rahbar: _________ f.m.f.doktori prof. D.Q.Durdiyev

Bajaruvchi: _________ M.D.Burxonov

JIZZAX – 2022
MUNDARIJA
Kirish………………………….……………………………………………………3

IBOB KASR TARTIBLI HOSILALAR ………………………………………19
1.1. Kaputo ma’nosidagi kasr tartibli hosila…………………………….……...19
1.2. Dirakning delta,Mittag Lefler funksiyasi va ularning xossalari…………….33
I Bob yuzasidan xulosa ………………………………………………………......36
II BOB INTEGRAL ALMASHTIRISHLAR……………………………….…37
2.1. Fure almashtirishi…………………………………………………………....37
2.2. Laplas almashtirishi……………………………………………………….....49
II Bob yuzasidan xulosa ………………………………………………….…........52
III KASR TARTIBLI DIFFUZIYA TENGLAMASANING FUNDAMENTAL YECHIMI……………………………………………………………………..….53
3.1. Fundamental yechim tushunchasi…………………………………….….…53
3.2. Bir jinsli bo‘lmagan kasr tartibli differiensial tenglama uchun
Koshi masalasi …………………….………………………………………...59
3.3. Kasr tartibli diffuziya tenglamasi fundamental yechimi……………………65
III Bob yuzasidan xulosa ………………………………………………….……...68