In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.

For applications demanding a high torque density and high speed capability, the flux switching permanent magnet machine is an excellent candidate. However, the double salient structure and nonlinear behavior increases the challenge to model the magnetic field distribution and torque output. To date, only the magnetic equivalent circuit (MEC) is employed to model the magnetic field in an analytical manner. However, the MEC method suffers from a coarse discretization and the need for a relative complex adjustment when rotor movement or a parametric sweep is considered. Therefore this paper discusses an alternative technique based on the harmonic or Fourier model which solves these difficulties.Index Terms-Boundary value problem, flux switching, Fourier analysis, permanent magnet machine.

With the emergence of energy related issues in the automotive sector, there is a tendency to find new efficient solutions to replace existing electrical machinery. One promising candidate is the flux switching permanent magnet machine (FSPMM). Due to its challenging structure and nonlinear characteristic, in the investigation of the machine, generally finite element method (FEM), and rarely the magnetic equivalent circuit (MEC), are implemented. The following paper introduces an alternative analytical modeling technique by means of a hybrid model, which combines the advantages of the MEC and the Fourier analysis.Index Terms-Flux switching, Fourier analysis, hybrid model, magnetic equivalent circuit, permanent magnet.

In this paper, we introduce a numerical and analytical study of the HIV-1 infection of CD4 + T-cells conformable fractional mathematical model. This model is studied analytically by Kudryashov and modified Kudryashov methods and numerically by finite difference method. A comparison between the results of the analytical and numerical methods is investigated. We also give some figures that show how accurate the solutions will be obtained from analytical and numerical methods.

The study of nonlinear phenomena associated with physical phenomena is a hot topic in the present era. The fundamental aim of this paper is to find the iterative solution for generalized quintic complex Ginzburg–Landau (GCGL) equation using fractional natural decomposition method (FNDM) within the frame of fractional calculus. We consider the projected equations by incorporating the Caputo fractional operator and investigate two examples for different initial values to present the efficiency and applicability of the FNDM. We presented the nature of the obtained results defined in three distinct cases and illustrated with the help of surfaces and contour plots for the particular value with respect to fractional order. Moreover, to present the accuracy and capture the nature of the obtained results, we present plots with different fractional order, and these plots show the essence of incorporating the fractional concept into the system exemplifying nonlinear complex phenomena. The present investigation confirms the efficiency and applicability of the considered method and fractional operators while analyzing phenomena in science and technology.

This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the considered model are derived. Various figures such as 3D and 2D surfaces with the selecting the suitable of parameter values are plotted.

No abstract

No abstract