In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Successive Differentiation (FSDM), and Novel Analytical (FNAM), have been introduced. These iterative methods are applied on types of Electrical RLC-Circuit Equations fractional-order. The fractional series approximation derived solutions can be established by using obtained coefficients. algorithm...

The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.

We propose and experimentally demonstrate a tunable fractional order photonic differentiator using an on-chip electrically tuned Mach-Zehnder interferometer (MZI) structure. The phase shift at the resonant frequency of the MZI varies when applying different voltages, which can implement the fractional differentiation. Due to the large 3-dB bandwidth of the MZI, the differentiator is expected to...

Fractional calculus (differentiation and integration of arbitrary order) arise naturally in various areas of applied science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelas...

This work deals with the simulation and discretization of continuous time models with fractional order differentiation or integration. It addresses the issue of direct discretization of analog fractional order systems followed by approximating the discretization result with an integer order transfer function or approximating the analog fractional order system with an integer analog order system...

Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the Tikhonov regularization problem. Then, we prop...

We study the properties of fractional differentiation with respect to the reflection symmetry in a finite interval. The representation and integration formulae are derived for symmetric and anti-symmetric fractional derivatives, both of the Riemann-Liouville and Caputo type. The action dependent on the left-sided Caputo derivatives of orders in the range (1,2) is considered and we derive the Eu...

Fractional directional integrals are the extensions of the Riemann-Liouville fractional integrals from oneto multi-dimensional spaces and play an important role in extending the fractional differentiation to diverse applications. In numerical evaluation of these integrals, the weakly singular kernels often fail the conventional quadrature rules such as Newton-Cotes and Gauss-Legendre rules. It ...

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...

We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional integration/differentiation of a white Gaussian noise. We study correlation properties of the approximation to fractional Gaussian noise and point to the peculiarities of per...