On a fractal LC-electric circuit modeled by local fractional calculus

Advanced Statistical Mechanics

Analytical and numerical solutions of electrical circuits described by fractional derivatives

Assessment of the Al–Fe–Ti system

In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville–Caputo, Caputo–Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order α is equal to 1.

https://www.mdpi.com/1099-4300/18/8/402/pdf

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

Series of (YBa2Cu3O7−δ)1−x(Al2O3)x samples have been prepared using solid state reaction method. Various amount of nano-sized Al2O3 particles (∼50 nm) were added with (x=0, 0.005, 0.01, 0.02, and 0.05). The microstructure and the morphology of the polycrystalline samples have been characterized by X-ray diffraction (XRD) and atomic force microscopy (AFM). The magneto-transport properties of these samples were investigated using resistance–temperature (R–T) and current–voltage (I–V) characteristics. All samples showed an orthorhombic structure with a tendency to transformation to tetragonal phase at higher levels of nanoparticles addition. The morphology of the surface of pure samples reveals a considerable number of weak-links, randomly oriented and clean grain boundaries. While in samples with nano inclusions, grain boundaries were filled with nanosized particle and have less number of weak-links. Significant enhancement of the superconducting critical current density Jc in applied magnetic field was observed due to nano Al2O3 inclusions. However, further increase in the value of x decreases the transition temperature Tc and the critical current density Jc. These results were interpreted in terms of the flux pinning mechanisms in granular superconducting networks which leads to a better basic understanding of the performance of YBCO system in high applied magnetic fields.

Polycrystalline YBa2Cu3O7−δ with Nano-sized Al2O3 Inclusions

We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the oscillatory behavior (LC circuit) go over to a decay behavior (RC circuit) as grows from 0 to 1, and vice versa. An explanation of the behavior is proposed based on the idea of the evolution of a resistive property in the inductor giving a new value to the inductance that affects the frequency of the oscillator. Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05

A Fractional LC − RC Circuit

Polycrystalline samples of Y 1− x Gd x Ba 2 Cu 3 O 7 with different Gd contents ( x =1,0.75,0.5,0.25) were prepared using the usual solid state reaction method. X-ray characterization of these samples showed an orthorhombic phase. The lattice parameters a , b , and c were found to increase with increasing Gd concentration which is due to the larger volume of Gd atoms. Magnetization and transport measurements show the same transition temperature of 91 K for all samples studied. Initial and magnetization hysteresis loop measurements showed that the paramagnetic behavior is dominant at high fields.

The paramagnetic contribution in the magnetization behavior of Y1−xGdxBa2Cu3O7

The Adventures of Hir and Ranjha, the immortal love story, is regarded as a classic of Punjabi literature. It speaks of the unbounded love that two souls have for each other, how they defy the taboos of their society, face the vicissitudes of fortune and yet remain true to each other. But they are also star-crossed lovers and ultimately united only in death. More than the story, it is the presentation of Waris that has immortalised the romance in the classical literature of India. The tragic love story of Hir and Ranjha has been a favourite theme with poets and writers for centuries. It was a well-known story that existed long before Waris Shah penned it down (around 1766) in the same way as the Faust legend existed long before Goethe.

The Adventures of Hir and Ranjha

Diabetic ketoacidosis is a known complication of diabetes mellitus. The annual incidence of diabetic ketoacidosis (DKA) among subjects with type 1 diabetes is between 1% and 5% in European and American series respectively. This incidence appears to have remained relatively constant over the last decade in western countries whereas 20-30% of cases occur in newly diagnosed patients. Mortality rate is reported less than 5% in experienced centres whereas internationally overall mortality is 1-10 percent. The objective of this study was to find out mortality rate in patients of diabetic ketoacidosis admitted to east medical ward of Mayo Hospital, Lahore. A descriptive retrospective study was conducted on patients admitted to East medical ward with the diagnosis of DKA. There were 44 patients included in this study. Regarding outcome of patients 84.1% of patients were discharged. The mortality was found to be 15.9% that is much higher as compared to other studies where it was around 5%.

M. K. Hasan

Papers

Polycrystalline YBa2Cu3O7−δ with Nano-sized Al2O3 Inclusions

A Fractional LC − RC Circuit

The paramagnetic contribution in the magnetization behavior of Y1−xGdxBa2Cu3O7

The Adventures of Hir and Ranjha

Mortality review of diabetic ketoacidosis in mayo hospital, lahore - pakistan