MAXSUS FUNKSIYALARNING KAST TARTIBLI HOSILALARDA TATBIQLARI VA ULARNING ASIMPTOTIK XOSSALARI
Keywords:
Kalit so‘zlar: Kasr tartibli hosila, maxsus funksiyalar, Mittag-Leffler funksiyasi, Prabhakar funksiyasi, Rayt funksiyasi, Foksning $H$-funksiyasi, Mellin- Barnes integrali, asimptotik yoyilma, anomal diffuziyaAbstract
KIRISH
Zamonaviy matematik modellashtirishda chiziqli bo‘lmagan, irsiy xususiyatga
va "xotira effekti"ga ega bo‘lgan jarayonlarni tavsiflashda kasr tartibli differensial
tenglamalar o‘rni beqiyosdir. Klassik butun tartibli hosilalardan farqli o‘laroq, kasr
tartibli anomal diffuziya, dissipativ mexanika va makroiqtisodiy dinamika kabi
jarayonlarni ifodalovchi tenglamalar yechimlari elementar funksiyalar (eksponenta,
sinus, kosinus) orqali emas, balki maxsus funksiyalar sinfi orqali aniq ifodalanadi.
References
Adabiyotlar
1. Kasr tartibli hisoblash va differensial tenglamalar nazariyasiga oid tadqiqotlar
to‘plami va maxsus funksiyalar tahlili qo‘lyozmasi, 2026. (Matn ichidagi
havolalar manbasi).
2. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and application of fractional
differetial equations. North–Holland Mathematical Studies, Amsterdam:
Elsevier, 2006.
3. Durdiev D. K., Turdiev H. H. Inverse coefficient problem for a time-fractional
wave equation with initial-boundary and integral type overdetermination
conditions // Mathematical Methods in the Applied Sciences. 2024. Vol. 47.
Issue 6. P. 5329–5340. https://doi.org/10.1002/mma.9867
