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

In this paper, we proposed a modified Hestenes-Stiefel (HS) conjugate
gradient method. This achieves a high order accuracy in approximating the second
order curvature information of the objective function by utilizing the modified
secant condition which is proposed by Babaie-Kafaki [1], also we derive a nonquadratic
conjugate gradient model. The important property of the suggestion
method that is satisfy the descent property and global convergence independent of
the accuracy of the line search. In addition, we prove the global convergence under
some suitable conditions, and we reported the numerical results under these
conditions.

The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

     This paper presents an analysis solution for systems of partial differential equations using a new modification of the decomposition method to overcome the computational difficulties. Convergence of series solution was discussed with two illustrated examples, and the method showed a high-precision, being a fast approach to solve the non-linear system of PDEs with initial conditions. There is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. The method does not require any discretization or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented, with high accuracy and rapid convergence to the exact solution,

This paper aims at introducing a new generalized differential operator and new subclass of analytic functions to obtain some interesting properties like coefficient estimates and fractional derivatives.

     The oscillation property of the second order half linear dynamic equation was studied, some sufficient conditions were obtained to ensure the oscillation of all solutions of the equation. The results are supported by illustrative examples.

Original Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio

     In this paper, we conduct some qualitative analysis that involves the global asymptotic stability (GAS) of the Neutral Differential Equation (NDE) with variable delay, by using  Banach contraction mapping theorem, to give some necessary conditions to achieve the GAS of the zero solution.

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.