FRACTIONAL DIFFERENTIAL AND INTEGRATING EQUATIONS BY NUMERICAL SOLUTION

The main objective of this paper is to investigate a new fractional mathematical model that includes a nonsingular derivative factor. The basic properties of the new model including non-negative, finite solution, numerical simulations are shown, and some discussions from mathematical perspectives are given. Then, the optimal control problem for the new model is determined by introducing several variables. Solving fractional order differential equations in an accurate, reliable, and efficient manner is more difficult than in the case of standard integer order; In addition, most computational tools do not provide built-in functionality for this type of problem. In this paper, we review two of the most effective numerical methods for solving fractional-order problems, Static and solving nonlinear systems included in the implicit. Methods. We, therefore, present a set of MATLAB procedures specifically designed to solve three families of partial order problems: partial differential equations (FDEs), Some examples are provided to illustrate the use of the procedures