Abstarct: In this research, by introducing the minimum length and its relation with Heisenberg uncertainty principle, we will investigate it with its modified form that is called generalized uncertainty principle. Therefore, its properties are introduced, also considering the generalized uncertainty principle of each of the observable operators, we have tried to rewritten them and by using it, the particles spin zero and spin half are inversigated1 + 1dimention, and the energy spectrum and their wave function are obtained in the ground and excited state. Finally, some of the proposed models for the generalized uncertainty principle are introduced and we have tried to obtain a general form of their Lagrangian and their Hamiltonian. In the end by using of the obtained Lagrangian equations of particle motion we obtained the equation of the motion for the particle that move under the introduced conditions and we obtained a nonlinear differential and we solved it by the Adomian method and we compared the obtained results with other accessible method. Also, we have obtained the ordinary cases when the deformation parameter tends to zero, all the results turn into ordinary results.