Comparative analysis of suitability of fractional derivatives in modelling the practical capacitor

Purpose The purpose of this paper is to compare the suitability of fractional derivatives in the modelling of practical capacitors. Such suitability refers to ability to provide the analytical capacitance function that matches the experimental ones of each fractional derivative. Design/methodology/approach The analytical capacitance functions based on various fractional derivatives of both local and nonlocal types including the author’s have been derived. The derived capacitance functions have been simulated and compared with the experimental ones of aluminium electrolytic and electrical double layer capacitors (EDLCs). Findings This paper has found that any local fractional derivative with fractional power law-based relationship with the conventional one is suitable for modelling the aluminium electrolytic capacitor (AEC) by incorporating with the conventional capacitance definition. On the other hand, the author’s nonlocal fractional derivatives have been found to be more suitable than the others for modelling the EDLC by incorporating with the revisited definition of capacitance. Originality/value The proposed comparative analysis has been originally presented in this work. The criterion for local fractional derivative, to be suitable for modelling the AEC, has been found. The nonlocal fractional operators which are most suitable for modelling the EDLC have been derived where the unsuitable one has been pointed out.

Solving Time Fractional Schrodinger Equation in the Sense of Local Fractional Derivative

The motivation of the studies solving the mathematical problems including time fractional Schrodinger equation by means of a method which is a combination of Chebyshev collocation method and Residual power series method (RPSM). The time fractional derivative in local fractional derivative sense is discretized with the help of Chebyshev collocation method to reduce time fractional Schrodinger equation into a system including two fractional ordinary differential equations. At this stage applying RPSM produce the truncated solution of the mathematical problem. Given examples illustrated that this method is applicable and compatible for solving mathematical problems with fractional derivative.

A new RLC series-resonant circuit modeled by local fractional derivative

The local fractional derivative has gained more and more attention in the field of fractal electrical circuits. In this paper, we propose a new ?-order RLC** resonant circuit described by the local fractional derivative for the first time. By studying the non-differentiable lumped elements, the non-differentiable equivalent imped?ance is obtained with the help of the local fractional Laplace transform. Then the non-differentiable resonant angular frequency is studied and the non-differentiable resonant characteristic is analyzed with different input signals and parameters, where it is observed that the ?-order RLC resonant circuit becomes the ordinary one for the special case when the fractional order ? = 1. The obtained results show that the local fractional derivative is a powerful tool in the description of fractal circuit systems.

Non-differentiable solutions of a family of modified Korteweg-Devries equations within local fractional derivative

In this paper, a family of modified Korteweg-de Vries equations within local fractional derivative are constructed, and their non-differentiable solutions are discussed by using several methods.