Some properties and applications of fractional differential equations

In this study, some definitions and properties of fractional derivative and integral in the literature are mentioned. After Adams-Bashforth method that is used to solve classical differential equations is presented, the usage of Lagrange and Newton polynomial methods are suggested for solving fractional differential equations. Some classical and fractional differential equations are solved numerically and simulations are presented for fractional derivatives of different order. Finally, the Bouali chaotic system is handled with fractional derivatives, and numerical simulations are given for the solution of this system. The behavior of such a model under classical and fractional derivatives can be seen with simulations. Keywords: Bouali chaotic system, fractional derivative, fractional integral, numerical algorithm.