Papers by Abdulla - Al - Mamun
Heliyon, 2020
The main intension of this paper is to extract new and further general analytical wave solutions ... more The main intension of this paper is to extract new and further general analytical wave solutions to the (2 þ 1)dimensional fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation in the sense of conformable derivative by implementing the advanced exp ðÀϕ ðξÞÞ-expansion method. This method is a particular invention of the generalized exp ðÀϕ ðξÞÞ-expansion method. By the virtue of the advanced exp ðÀϕ ðξÞÞ-expansion method, a series of kink, singular kink, soliton, combined soliton, and periodic wave solutions are constructed to our preferred space time-fractional (2 þ 1)-dimensional AKNS equation. An extensive class of new exact traveling wave solutions are transpired in terms of, hyperbolic, trigonometric, and rational functions. To express the underlying propagated features, some attained solutions are exhibited by making their three-dimensional (3D), twodimensional (2D) combined, and 2D line plot with the help of computational packages MATLAB. All plots are given to show the proper wave features through the founded solutions to the studied equation with particular preferring of the selected parameters. Moreover, it may conclude that the attained solutions and their physical features might be helpful to comprehend the water wave propagation in water wave mechanics.
International Journal of Scientific & Engineering Research, 2020
In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to so... more In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra's integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it's exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.
International Journal of Modern Physics and Applications, 2019
This design is a pneumatic loading and unloading manipulator, through the relevant literature rev... more This design is a pneumatic loading and unloading manipulator, through the relevant literature review and collation and market research, the design of the manipulator has four degrees of freedom, and the use of circular coordinates form of design. This kind of manipulator has the characteristics of wide application range and simple operation. Through the design and analysis of the pneumatic loop, the motion mode of the manipulator is determined, and the specific motion of each part is described. This paper mainly designs three main parts of the manipulator, which are finger, wrist and arm. The structure of each part is designed and the working structure of the whole manipulator is determined. The manipulator has two kinds of replaceable functions, which can grasp bar or other rules of fast material, and can also load and unload sheet material. The hand is designed as a replaceable structure, with a clamping and adsorption structure; the rotary cylinder of the wrist is designed; the forehead expansion and lifting mechanism of the arm and the rotating motion of the hydraulic buffer arm is connected by two cylinders and two throttle dampers. It's buffers are introduced. The driving torque of each structure is calculated and the design and calculation of each cylinder are carried out.
International Journal of Mathematics and Computational Science, 2019
In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to so... more In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the eighth order boundary value problems. It is to be mentioned that, presently, the literature on the numerical solutions of eighth order boundary value problem and associated eigen value problems is not available. By using a suitable transformation, the variational iteration method can be used to show that eighth order boundary value problems are equivalent to a system of integral equation. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it's exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with exact solution. Finally, we investigate the error between numerical solution and exact solution and draw the graph of error function by using Mathematica.
International Journal of Mathematics and Computational Science, 2019
In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to so... more In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the seventh order boundary value problems. It is to be mentioned that, presently, the literature on the numerical solutions of seventh order boundary value problem and associated eigen value problems is not available. By using a suitable transformation, the variational iteration method can be used to show that seventh order boundary value problems are equivalent to a system of integral equation. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it's exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with exact solution. Finally, we investigate the error between numerical solution and exact solution and draw the graph of error function by using Mathematica.
International Journal of Scientific & Engineering Research, 2018
In this paper, we investigate second order parabolic partial differential equation of a 1D heat e... more In this paper, we investigate second order parabolic partial differential equation of a 1D heat equation. In this paper, we discuss the derivation of heat equation, analytical solution uses by separation of variables, Fourier Transform and Laplace Transform. Finally, we consider a problem of heat equation and the solution of this problem implement in computer programming.
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Papers by Abdulla - Al - Mamun