Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport.

The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model (also known as the Debye-Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order , and the second-order space derivative with the Riesz-Feller fractional derivative of order . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox's H-function that we evaluate for different values of and .

Fractional Marcus-Hush-Chidsey-Yakopcic current-voltage model for redox-based resistive memory devices.

We propose a circuit-level model combining the Marcus-Hush-Chidsey electron current equation and the Yakopcic equation for the state variable for describing resistive switching memory devices of the structure metal-ionic conductor-metal. We extend the dynamics of the state variable originally described by a first-order time derivative by introducing a fractional derivative with an arbitrary order between zero and one. We show that the extended model fits with great fidelity the current-voltage characteristic data obtained on a Si electrochemical metallization memory device with Ag-Cu alloy.

Possibility of information encoding/decoding using the memory effect in fractional-order capacitive devices.

In this study, we show that the discharge voltage pattern of a supercapacitor exhibiting fractional-order behavior from the same initial steady-state voltage into a constant resistor is dependent on the past charging voltage profile. The charging voltage was designed to follow a power-law function, i.e.

On the mechanistic pathways of exfoliation-and-deposition of graphene by bipolar electrochemistry.

Amongst the different graphene fabrication techniques, bipolar electrochemistry (BPE) has been recently reported as a simple, controllable, low cost, eco-friendly, and scalable method. It consists of a wirelessly placed carbon source between two feeding electrodes subjected to direct current (DC) voltage in a deionized water bath. Although the physicochemical characteristics of produced graphene have been evaluated, the exfoliation and deposition mechanisms are still unclear.