Article
Ufa Mathematical Journal
Volume 11, Number 2, pp. 19-33
Difference schemes for partial differential equations of fractional order
Bazzaev A.K., Tsopanov I.D.
DOI:10.13108/2019-11-2-19
Download PDF
Article on MathNetAbstact
Nowadays, fractional differential
equations arise while describing physical systems with such properties as power nonlocality, long-term memory and fractal property. The order of the fractional derivative is determined by the dimension of the fractal. Fractional mathematical calculus in the theory of fractals and physical systems with memory and non-locality becomes as important as classical analysis in continuum mechanics.
In this paper we consider higher order difference schemes of
approximation for differential equations with fractional-order
derivatives with respect to both spatial and time variables. Using the maximum principle, we obtain apriori estimates and prove the stability and the uniform convergence of difference schemes.