On study the existing result for the time fractional equation using the topological degree method

In this article, we suggest introducing the Riemann-Liouville time fractional derivative to a fractional equation (FPDE) involving a fractional Laplacian. Our work is divided into two parts. In the first part, the existence and uniqueness of time fractional linear equations are demonstrated, and the Galerkin approach is proposed to deal with them. In the second part, we investigate the existence results of the time fractional semilinear equation. To solve This problem, the Leray-Schauder degree method has been used with some conditions on the semilinear term.

Keywords:

Time fractional derivative , Galerkin method , Leray-Schauder degree , Riemann-Liouville derivative , fractional semilinear parabolic equation