This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

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

Nowadays, Wheeled Mobile Robots (WMRs) have found many applications as industry, transportation, inspection, and other fields. Therefore, the trajectory tracking control of the nonholonomic wheeled mobile robots have an important problem. This work focus on the application of model-based on Fractional Order  PI^aD^b (FOPID) controller for trajectory tracking problem. The control algorithm based on the errors in postures of mobile robot which feed to FOPID controller to generate correction signals that transport to  torque for each driven wheel, and by means of dynamics model of mobile robot these torques used to compute the linear and angular speed to reach the desired pose. In this work a dynamics model of

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems in

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.