An approximate method for solving fractional partial differential equation by using an embedding process

Abstract

In this article, solving of fractional partial differential equation (FPDE) with optimal time control approach is developed. Conformable derivative as a new definition of fractional derivative is considered. At first the (FPDE) with stationary regime is converted to optimal time control problem, then by using an embedding process, the obtained system is converted to finite-dimensional linear programming (LP) problem and finally optimal time corresponded by (FPDE) system is approximated. For example, this method is used on the conformable fractional heat equation with the initial and boundary conditions.