Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by ϕ6-modal expansion method

The current study deals with the exact solutions of nonlinear confirmable time fractional Sobolev type equations. Such equations have applications in thermodynamics, the flow of fluid through fractured rock. The underlying models are 2D equation of a semi-conductor with heating and Sobolev equation in 2D unbounded domain. These equation are used to describe the different aspects in semi-conductor. The analytical solutions of underlying models is not addressed yet or it is difficult to find. We gain the exact solutions of such models with help of analytical technique namely ϕ6-model expansion method. The abundant families of solutions are obtained by the Jacobi elliptic function and it will give us soliton and solitary wave solutions. So, we extract the different types of solutions such as, dark, bright, singular, combine, periodic and mixed periodic. The unique physical problems are selected from a variety of the solutions that will help the reader for the verification and data experiment. The graphical behavior of the underlying models is represented in the form of 3D, line graphs and their corresponding contours for the various values of the parameters.