A NEW TECHNIQUE FOR APPROXIMATE SOLUTION OF FRACTIONAL-ORDER PARTIAL DIFFERENTIAL EQUATIONS

In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs.

On the Application of Homotopy Analysis Method to Fractional Differential Equations

In this paper, an attempt has been made to obtain the solution of linear and nonlinear fractional differential equations by applying an analytic technique, namely the homotopy analysis method (HAM). The fractional derivatives are described by Caputo’s sense. By this method, the solution considered as the sum of an infinite series, which converges rapidly to exact solution with the help of the nonzero convergence control parameter ℏ. Some examples are given to show the efficiently and accurate of this method. The solutions obtained by this method has been compared with exact solution. Also our graphical represented of the solutions have been given by using MATLAB software.

Design and development of anchoring positioning control system for riprap leveling ship

It is very important to level foundation bed by riprap in water and soil engineering. In this paper, a real-time feedback convergence control method is proposed to control the position and heading angle of the riprap leveling ship. The wind, wave, current and hydrodynamic parameters are obtained by empirical formula; the tension of four cables is calculated according to the balance equation of six degrees of freedom, and then the cable deformation is obtained. According to the deformation of the cable, the length of the cable in a certain equilibrium state can be obtained. The length of four cables can be lengthened or shortened by comparing the length of cables at two balanced positions. The length of cables can be controlled by winch to complete the anchoring and positioning control of leveling ship.

Quantitative evaluation of industrial and commercial management’s promotion to economic growth based on hierarchical constraints

In order to improve the quantitative evaluation ability of industrial and commercial management on promoting economic growth, the design method of quantitative evaluation model of industrial and commercial management on promoting economic growth based on hierarchical constraints is proposed. the descriptive statistical analysis method to realize big data fusion mining for quantitative evaluation of business administration’s promotion to economic growth is used, and a hierarchical constraint parameter analysis model to realize node deployment model design of hierarchical constraint parameter analysis model is designed, fuzzy control and adaptive feature parameter identification are realized in the process of quantitative evaluation of industrial and commercial administration’s promotion to economic growth. Convergence control is realized in the process of quantitative evaluation based on pattern recognition and association distributed fusion. Fuzzy degree identification and optimization prediction of quantitative evaluation of industrial and commercial administration’s promotion to economic growth are realized in hierarchical constraint parameter analysis model. The simulation results show that the output accuracy and system stability of the quantitative evaluation of the promotion of business administration to economic growth are good.