A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h, is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model.

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density.

To evaluate changes in the Soil Organic Carbon (SOC) index, one of the key indicators of land degradation neutrality, soil carbon modeling is of primary importance. In litera-ture, the analysis has been focused on the stability characterization of soil carbon steady states and in the calculation of the resilience of the stable equilibria. Neither stability nor resilience, however, provide any information about transient dynamics, and models with highly resilient equilibria can exhibit dramatic transient responses to perturbations.

Recent literature confirms the crucial influence of non-viscous deformations together with temperature impact on glacier and rock glacier flow numerical simulation. Along this line, supported by the successful test on a one-dimensional set-up developed by two of the author, we propose the numerical solution of a two-dimensional rock-glacier flow model based on an ice constitutive law of second grade differential type .

Regular physical exercise and appropriate nutrition affect metabolic and hormonal responses and may reduce the risk of developing chronic non-communicable diseases such as high blood pressure, ischemic stroke, coronary heart disease, some types of cancer, and type 2 diabetes mellitus. Computational models describing the metabolic and hormonal changes due to the synergistic action of exercise and meal intake are, to date, scarce and mostly focussed on glucose absorption, ignoring the contribution of the other macronutrients.

Usually, clinicians assess the correct hemodynamic behavior and fetal wellbeing during the gestational age thanks to their professional expertise, with the support of some indices defined for Doppler fetal waveforms. Although this approach has demonstrated to be satisfactory in the most of the cases, it can be largely improved with the aid of more advanced techniques, i.e. numerical analysis and simulation. Another key aspect limiting the analysis is that clinicians rely on a limited number of Doppler waveforms observed during the clinical examination.

During melting under gravity in the presence of a horizontal thermal gradient, buoyancy-driven convection in the liquid phase affects significantly the evolution of the liquid-solid interface. Due to the obvious engineering interest in understanding and controlling melting processes, fluid dynamicists and applied mathematicians have spent many efforts to model and simulate them numerically. Their endeavors concentrated in the twenty-five years period between the publication of the paper by Brent, Voller & Reid (1988) and that by Mansutti & Bucchignani (2011).