Ercília Sousa is a Full Professor in the Department of Mathematics at the University of Coimbra, where she also completed her degree in pure mathematics. After receiving a DPhil from the University of Oxford, on numerical analysis, she joined the Research Center for Mathematics at the University of Coimbra. Her research interests are broadly in numerical analysis and partial differential equations, with a recent focus on numerical methods for fractional diffusion equations.

• Prelude.- Fractional derivatives: fundamental concepts.- A governing equation for Lévy flights.- Consistency, stability and convergence of numerical methods.- Fractional differential equations in unbounded domains.- Fractional differential equations in bounded domains: absorbing boundaries.- Fractional differential equations in bounded domains: reflecting boundaries.- The road ahead.- References.

Ercília Sousa is a Full Professor in the Department of Mathematics at the University of Coimbra, where she also completed her degree in pure mathematics. After receiving a DPhil from the University of Oxford, on numerical analysis, she joined the Research Center for Mathematics at the University of Coimbra. Her research interests are broadly in numerical analysis and partial differential equations, with a recent focus on numerical methods for fractional diffusion equations.

• Prelude.- Fractional derivatives: fundamental concepts.- A governing equation for Lévy flights.- Consistency, stability and convergence of numerical methods.- Fractional differential equations in unbounded domains.- Fractional differential equations in bounded domains: absorbing boundaries.- Fractional differential equations in bounded domains: reflecting boundaries.- The road ahead.- References.

Ercília Sousa is a Full Professor in the Department of Mathematics at the University of Coimbra, where she also completed her degree in pure mathematics. After receiving a DPhil from the University of Oxford, on numerical analysis, she joined the Research Center for Mathematics at the University of Coimbra. Her research interests are broadly in numerical analysis and partial differential equations, with a recent focus on numerical methods for fractional diffusion equations.

• Prelude.- Fractional derivatives: fundamental concepts.- A governing equation for Lévy flights.- Consistency, stability and convergence of numerical methods.- Fractional differential equations in unbounded domains.- Fractional differential equations in bounded domains: absorbing boundaries.- Fractional differential equations in bounded domains: reflecting boundaries.- The road ahead.- References.