The solution of the anomalous diffusion equation by a finite element method formulation based on the Caputo derivative

A finite element method formulation is developed for the solution of anomalous diffusion equation. This equation belongs to branch mathematics called fractional calculus: it governed by a partial differential in which time derivative, whose order ranges interval (0,1), replaces first-order derivative classical In this work, Caputo integro-differential operator employed represent derivative. After assuming linear variation variable interest, say u, intervals overall discretized, integral computed analytically. To demonstrate usefulness proposed formulation, four examples are analysed, showing good agreement between FEM results analytical solutions, even small orders