On the computation of an integral of the modified Bessel function, ∫x∞dλλμKν(λ)

•Numerical scheme to evaluate ∫x∞dλλμKν(λ) has been introduced.•Transient diffusion in fractal structures.•Scheme is used to compute the response at a fractured well.

The work introduces a simple numerical scheme to evaluate the integral ∫x∞dλλμKν(λ) where Kν(λ)Kν(λ) is the modified Bessel function of fractional order. We use this scheme to compute the response at a fractured well that describes transient diffusion in porous media considered to be fractal structures.