In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Observation of the e/3 fractionally charged Laughlin quasiparticles. Abstract The existence of fractional charges carrying the current is experimentally demonstrated. Using a 2-D electron system in high perpendicular magnetic field we measure the shot noise associated with tunneling in the fractional quantum Hall regime at Landau level filling factor 1/3. The noise gives a direct determination ...

This paper reviews tunnel spectroscopy of fractional quantum Hall edges using cleaved-edge overgrown devices. Beginning with an intuitive introduction to various experimental and theoretical aspects, the device structure is reviewed, and the experimental result of a continuum of powerlaw tunneling exponents is revisited. The unanticipated behavior of the exponent with fractional filling factor ...

The magnetic flux threading a conventional superconducting ring is typically quantized in units of Φ0=hc/2e. The factor of 2 in the denominator of Φ0 originates from the existence of two different types of pairing states with minima of the free energy at even and odd multiples of Φ0. Here we show that spatially modulated pairing states exist with energy minima at fractional flux values, in part...

We have experimentally evidenced an elementary charge fission, in which an elementary charge in an integer quantum Hall (IQH) system breaks up into fractional charges at a local fractional quantum Hall (FQH) state. Shot-noise measurements establish the e/3-charge of tunneling quasiparticles through the local FQH state, which is prepared in a low-density region near a quantum point contact (QPC)...

Recently we have developed an efficient flexible multirate signal processing structure with high oversampling ratio and adjustable fractional or irrational sampling rate conversion factor. One application area is a multistandard communication receiver which should be adjustable for different symbol rates utilised in different systems. The proposed decimation filter consists of parallel CIC (cas...

Rats bearing the Yoshida AH-130 ascites hepatoma showed enhanced fractional rates of protein degradation in gastrocnemius muscle, heart, and liver, while fractional synthesis rates were similar to those in non-tumor bearing rats. This hypercatabolic pattern was associated with marked perturbations of the hormonal homeostasis and presence of tumor necrosis factor in the circulation. The daily ad...

Non-regular two-level fractional factorial designs, such as Plackett–Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of nonregular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular twolevel fractional factorial designs whose run size is always a power of 2 (4, ...