An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem

This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald–Letnikov sense. The method is based on the linear programming problem. In this paper, by using first the concept of fractional derivatives, we will suggest a method where an equation with a fractional derivative is changed to a linear programming problem, and by solving it the fractional derivative will be obtained. Actually this suggested method is based on the minimization of total error. Some numerical examples are provided to confirm the accuracy of the proposed method.