Due to the dispersive porous nature of its material, carbon–carbon supercapacitors have a current–voltage relationship which is modeled by a fractional-order differential equation of the form i(t)=Cα[Formula presented] where α≤1 is a dispersion coefficient and Cα is a pseudo-capacitance not measurable in Farads. Hence, the energy stored in a capacitor, known to equal CV2/2 where C is the capacitance in Farad and V is the voltage applied, does not apply to a supercapacitor. In a recent work (Allagui et al., 2016), a fractional-order energy equation that enables the quantification of the energy

Plasmonic photovoltaics (PVs) are promising structures that improve thin-film photovoltaics performance, where optical absorption is improved via embedding metallic nanoparticles in the PV's active layer to trap the incident optical wave into the photovoltaic cell. The presented work investigates the design of PV with both structures of conical and cylindrical metallic nanoparticles through studying their extinction cross-sections and electric field distributions. Also, the impact of these nanoparticles in silicon PVs on the optical absorption enhancement is investigated. The figure of merit