Keywords
Abstract
Ushbu maqolada kasr darajali differensial tenglamalar va ularning zamonaviy matematik modellashtirishdagi ahamiyati o‘rganiladi. Kasr tartibli differensial operator tushunchasi, Riman–Lyuvill va Kaputo hosilalarining asosiy ta’riflari hamda ularning o‘ziga xos xususiyatlari yoritiladi. Kasr darajali differensial tenglamalarning klassik differensial tenglamalardan farqli jihatlari tahlil qilinib, xotira effektiga ega bo‘lgan jarayonlarni modellashtirishdagi imkoniyatlari ko‘rsatiladi. Shuningdek, bunday tenglamalarning yechimlarini ifodalashda Mittag–Leffler funksiyasining o‘rni va kasr tartibli modellarning fizika, mexanika hamda boshqa fanlardagi tatbiqlari bayon etiladi.
References
Podlubny I. Fractional Differential Equations. Academic Press, San Diego, 1999.
2. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
3. Diethelm K. The Analysis of Fractional Differential Equations. Springer, Berlin, 2010.
4. Samko S.G., Kilbas A.A., Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, 1993.