This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

The main purpose of this paper, is to characterize new admissible classes of linear operator in terms of seven-parameter Mittag-Leffler function, and discuss sufficient conditions in order to achieve certain third-order differential subordination and superordination results. In addition, some linked sandwich theorems involving these classes had been obtained.  

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.

This paper proposes a new structure for a Fractional Order Sliding Mode Controller (FOSMC) to control a Twin Rotor Aerodynamic System (TRAS). The new structure is composed by defining two 3-dimensional sliding mode surfaces for the TRAS model and introducing fractional order derivative integral in the state variables as well as in the control action. The parameters of the controller are determined so as to minimize the Integral of Time multiplied by Absolute Error (ITAE) performance index. Through comparison, this controller outperforms its integer counterpart in many specifications, such as reducing the delay time, rise time, percentage overshoot, settling time, time to reach the sliding surface, and amplitude of chattering in control inpu

Blockchain represents a new promising technology with a huge economic impact resulting from its uses in various fields such as digital currency and banking; malware represents a serious threat to users, and there are many differences in the effectiveness of antivirus software used to deal with the problem of malware. This chapter has developed a coefficient for measuring the effectiveness of antivirus software. This chapter evaluates the effectiveness of antivirus software by conducting tests on a group of protection programs using a folder containing an amount of data. These programs are applied to combat viruses contained in this folder. The study revealed that the effectiveness of antivirus software is as follows: AVG scored 0%,

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.

The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S