Temporal evolution for <i>t</i> ∈ [0,400 ms] of the standard solution with reduced conductivity and the fractional solution with unit conductivity parameter at three equally spaced nodes <i>P</i>₁, <i>P</i>₂, <i>P</i>₃, in the spatial domain [0, 1 cm].

<p>The continuous blue line corresponds to the standard solution obtained with <i>α</i> = 2, <i>D</i> = 0.093 mS⋅cm⁻¹. The dashed red line represents the fractional solution obtained by setting <i>α</i> = 1.5, <i>D</i> = 1 mS⋅cm⁻¹. In both cases the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

Temporal profile for <i>t</i> ∈ [0,500 ms] of the solution obtained with ten different values of <i>α</i> at the mid-point of the spatial domain [0, 1 cm].

<p>In all cases the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

APD dispersion at forty-eight equally spaced nodes in [0.06 cm, 1 cm] for ten different values of <i>α</i>.

<p>For a fixed <i>α</i>, the APD is computed from the AP solution profile recorded at each considered node in the spatial interval. Dispersion of APD is then defined as the difference between the computed value of APD at that node and the maximum APD value recorded for the same value of <i>α</i> over the entire spatial domain.</p

The four relative metrics as a function of the key parameter Δ<i>t</i> (the time step), for four selected values of <i>α</i>.

<p>The solution is computed for all values of <i>α</i> on the time interval [0,500 ms] with <i>N</i> = 400. All relative errors are evaluated by comparing the solution for a specific combination of <i>α</i> and Δ<i>t</i> with the solution obtained for the same <i>α</i> when Δ<i>t</i> = 6.25⋅10⁻⁴ ms. In all simulations, the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

Activation time of forty-eight equally spaced nodes in the spatial domain [0.06 cm, 1 cm] and conduction velocity for ten different values of <i>α</i>.

<p>The CV corresponding to the reciprocal of the gradient of each of the ten straight lines in (A) was considered as data in (B) and a quadratic dependence of these data points from the fractional order <i>α</i> was established.</p

Curve fitting of three data sets obtained from the AP solution profile at the node <i>P</i>₂ for ten different values of <i>α</i> ∈ (1, 2].

<p>(A) AP depolarization peak height, (B) dome peak height, (C) early repolarization minimum.</p

AP foot of the solution profile obtained at the node <i>P</i>₂ for ten different values of <i>α</i> ∈ (1, 2].

<p>To aid the visualisation of the differences produced by varying the fractional order, we align the AP foot of the ten solution profiles considered so that the activation time (AT) of the node <i>P</i>₂ coincides for all values of <i>α</i>.</p

The four relative metrics as a function of the key parameter <i>N</i> (the number of eigenfunctions), for four selected values of <i>α</i>.

<p>The solution is computed for all values of <i>α</i> on the time interval [0,500 ms] with a uniform time step Δ<i>t</i> = 0.01 ms. All relative errors are evaluated by comparing the solution for a specific combination of <i>α</i> and <i>N</i> with the solution obtained for the same <i>α</i> when <i>N</i> = 3200. In all simulations, the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p