This paper proposes a new concept of random-order fractional differential equation model, in which a noise term is included in the fractional order. We investigate both a random-order anomalous relaxation model and a random-order time fractional anomalous diffusion model to demonstrate the advantages and the distinguishing features of the proposed models. From numerical simulation results, it i...

In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The ...

This paper describes a delta-sigma ( A-Z ) modulation and fractional-S frequency division technique to perform indirect digital frequency synthesis based on the use of a phaselocked loop (PLL). The use of 1 Y modulation concepts results in a beneficial noise shaping of the phase noise (jitter) introduced by fractional-S division. The technique has the potential to provide low phase noise, fast ...