This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

In this work, polyvinylpyrrolidone (PVP), Multi-walled carbon nanotubes (MWCNTs) nanocomposite was prepared and hybrid with Graphene (Gr) by casting method. The morphological and optical properties were investigated. Fourier Transformer-Infrared (FT-IR) indicates the presence of primary distinctive peaks belonging to vibration groups that describe the prepared samples. Scanning Electron Microscopy (SEM) images showed a uniform dispersion of graphene within the PVP-MWCNT nanocomposite. The results of the optical study show decrease in the energy gap with increasing MWCNT and graphene concentration. The absorption coefficient spectra indicate the presence of two absorption peaks at 282 and 287 nm attributed to the π-π* electronic tr

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

Magnetic levitation (Maglev) systems are employed in a wide range of applications and are therefore of significant practical importance, which has led to growing research interest. This paper presents the design of a terminal synergetic control (TSC) and feedback linearization-based proportional-integral-derivative plus second-order derivative (FL-PIDD2) controller for the Maglev system. For developing the control law of both controllers, the mathematical model of the Maglev system is converted into a canonical system where the expression of the nonlinearity is displayed in the last differential dynamic equation of the system. The determination of the TSC and FL-PIDD2 gains for achieving the desired dynamic response is carried out using the