O‘ZBEKISTON RESPUBLIKASI OLIY TA’LIM, FAN VA INNOVATSIYALAR VAZIRLIGI NAMANGAN DAVLAT UNIVERSITETI MATEMATIK ANALIZ KAFEDRASI
“DAK ga tavsiya etaman” Magistratura bo‘limi boshlig‘i _______________R.Jalalov “___”___________2023-yil
“DAK ga tavsiya etaman” Matematik analiz kafedrasi mudiri __________ A. Mashrabboyev “___”___________2023-yil
MAMADALIYEV AZIMJON USUBJON O‘G‘LI KASR TARTIBLI DIFFERENSIAL TENGLAMALAR UCHUN BOSHLANG’ICH MASALA 70540101 – Matematika (Differensial tenglamalar va matematik fizika) Magistr akademik darajasini olish uchun yozilgan
DISSERTATSIYA
Ilmiy rahbar: f.-m.f.d., prof. Karimov E.T
NAMANGAN-2023
Annotatsiya Ushbu dissertatsiya ishi kasr tartibli differensial tenglamalar uchun Koshi masalalarini tadqiq etishga bagʻishlangan boʻlib, unda umumlashgan boshlangʻich shartli masala Hilfer kasr tartibli hosilasi ishtirok etgan differensial tenglama uchun oʻrganilgan va bu masalaning tatbiq etib shunday boshlangʻich shartli chegaraviy masala sub-diffuziya tenglamasi uchun oʻrganilgan. Bundan tashqari, umumlashgan kasr tartibli hosila ishtirok etgan differensial tenglama uchun ham Koshi masalasining yechimi bir qiymatli topilib, bu masalaning tatbigʻi sifatida shunday hosila ishtirok etgan xususiy hosilali differensial tenglama uchun chegaraviy masala tadqiq etilgan.
Abstract The present dissertation work is devoted to the studying of Cauchy problems for fractional differential equations. In fact, problem with generalized initial condition for differential equation with the Hilfer fractional derivative is studied and applying the solution of this problem, the boundary problem for sub-diffusion equation was studied, as well. Moreover, the Cauchy problem for differential equation involving generalized fractional derivative was studied for a unique solvability and its solution was applied to studying boundary problem for partial differential equation involving generalized fractional derivative.
