Fractional Model of Plasma Oscillation

Fractional calculus of non-integer order provides a powerful method in the modelling of physical system with spatial complexity and with complex time-dependent dynamics which results in memory and nonlocal effects. Some recent applications include the construction of fractional models to account for the surface roughness for electron emission1,2 and light absorption3, and spatial disorderness4 for charge transport. In this work, we intend to account for the memory and non-local effects of the collective oscillation of electrons in a plasma environment, namely a fractional model plasma oscillation is constructed. The effect of plasma frequency will be studied in terms of a fractional parameter.