Matrix approach to discrete fractional calculus II: Partial fractional differential equations

• Published in: Journal of computational physics Vol. 228; no. 8; pp. 3137 - 3153
• Main Authors: Podlubny, Igor, Chechkin, Aleksei, Skovranek, Tomas, Chen, YangQuan, Vinagre Jara, Blas M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.05.2009; Elsevier
• Subjects: Calculus; Computational techniques; Delay; Derivatives; Differential equations; Differential equations with delays; Diffusion; Discretization; Exact sciences and technology; Fractional diffusion equation; Fractional partial differential equations; Integers; Mathematical analysis; Mathematical methods in physics; Mathematical models; Numerical methods; Physics; 65Z05; Differential equations with delays; Discretization; 65M06; Numerical methods; 65D25; Fractional diffusion equation; Fractional partial differential equations; 91B82; Partial differential equations; Numerical method; Fractional derivative; Calculation methods; Space-time; Numerical solution; Differential equations; S matrix; Diffusion equation; Calculation

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested me...