English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The aim of this work is to devise and analyse an accurate numerical scheme tosolve Erd\'elyi-Kober fractional diffusion equation. This solution can bethought as the marginal pdf of the stochastic process called the generalizedgrey Brownian motion (ggBm). The ggBm includes some well-known stochasticprocesses: Brownian motion, fractional Brownian motion and grey Brownianmotion. To obtain convergent numerical scheme we transform the fractionaldiffusion equation into its weak form and apply the discretization of theErd\'elyi-Kober fractional derivative. We prove the stability of the solutionof the semi-discrete problem and its convergence to the exact solution. Due tothe singular in time term appearing in the main equation the proposed methodconverges slower than first order. Finally, we provide the numerical analysisof the full-discrete problem using orthogonal expansion in terms of Hermitefunctions.

Numerical scheme for Erd\'elyi-Kober fractional diffusion equation using Galerkin-Hermite method