Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-...

In order to solve the local fractional differential equations, we couple residual method with Adomian decomposition via calculus operator. Several examples are given illustrate solution process and reliability of method.

In order to improve the correlation accuracy of correlation algorithm, the fractional order correlation algorithm of uncertain time sequences is proposed in this paper. By taking advantage of the memory property of fractional order, the algorithm introduces the measurement of fractional order differential for the local trend of time sequence into the correlation algorithm and also analyzes the ...

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional mater...