Abstract
Mazkur maqolada kasr tartibli hosilalarning matematik mohiyati va ularning fizikaviy jarayonlarni modellashtirishdagi ustunliklari tahlil qilinadi. An’anaviy differensial tenglamalarga nisbatan kasr tartibli hosilalar orqali turli tabiiy va texnik tizimlardagi inertsiya, diffuziya va xotira effektlari aniqlik bilan ifodalanadi. Shuningdek, maqolada kasr tartibli differensial tenglamalarning yechim usullari va real tizimlarga tatbiqlari ko‘rib chiqiladi.
References
1. Podlubny I. Fractional Differential Equations. – San Diego : Academic Press, 1999. – 340 p.
2. Mainardi F. Fractional Calculus and Waves in Linear Viscoelasticity. – London : Imperial College Press, 2010. – 368 p.
3. Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach // Physics Reports. – 2000. – Vol. 339, No. 1. – P. 1–77.
4. Tarasov V.E. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. – Berlin : Springer, 2011. – 505 p.
5. Oldham K.B., Spanier J. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. – New York : Academic Press, 1974. – 279 p.
6. Diethelm K. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. – Berlin : Springer, 2010. – 247 p.
7. Li C., Zeng F. Numerical Methods for Fractional Calculus. – Boca Raton : CRC Press, 2015. – 360 p.

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