Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives' compiled and edited by Giuseppe Failla and Massimiliano Zingales

Fractional calculus is a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, studies have shown that fractional operators can successfully describe challenging phenomena as viscoelasticity, diffusion in porous media, heat transfer, wave propagation, which can hardly be captured by classical differential calculus. Further, fractional calculus has proved to be an excellent framework for modelling nonconventional media, including fractal and non-local ones, opening valuable prospects on future engineered materials. This theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media, highlighting the considerable potential of fractional calculus to address several challenges of materials modelling.

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Advanced materials modelling via fractional calculus: challenges and perspectives
Published:11 May 2020Article ID:20200050


Research articles
On the thermodynamical restrictions in isothermal deformations of fractional Burgers model
Published:11 May 2020Article ID:20190278

Research articles
Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids
Published:11 May 2020Article ID:20190284

Research articles
Application of fractional calculus methods to viscoelastic behaviours of solid propellants
Published:11 May 2020Article ID:20190291

Research articles
Fractional-order modelling of epoxy resin
Published:11 May 2020Article ID:20190292

Research articles
A novel approach to nonlinear variable-order fractional viscoelasticity
Published:11 May 2020Article ID:20190296

Research articles
Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee
Published:11 May 2020Article ID:20190294

Research articles
Fractional thermoelasticity problem for an infinite solid with a penny-shaped crack under prescribed heat flux across its surfaces
Published:11 May 2020Article ID:20190289

Research articles
Fractional-order heat conduction models from generalized Boltzmann transport equation
Published:11 May 2020Article ID:20190280

Research articles
Effect of adsorption, radioactive decay and fractal structure of matrix on solute transport in fracture
Published:11 May 2020Article ID:20190283

Research articles
Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete
Published:11 May 2020Article ID:20190538

Research articles
Variable-order particle dynamics: formulation and application to the simulation of edge dislocations
Published:11 May 2020Article ID:20190290

Research articles
Energy dissipation for hereditary and energy conservation for non-local fractional wave equations
Published:11 May 2020Article ID:20190295

Research articles
Thermo-poromechanics of fractal media
Published:11 May 2020Article ID:20190288

Research articles
Impact force and moment problems on random mass density fields with fractal and Hurst effects
Published:11 May 2020Article ID:20190591