Global Existence and Uniqueness of Solution of Atangana–Baleanu Caputo Fractional Differential Equation with Nonlinear Term and Approximate Solutions

In this paper, a class of fractional order differential equation expressed with Atangana–Baleanu Caputo derivative with nonlinear term is discussed. The existence and uniqueness of the solution of the general fractional differential equation are expressed. To present numerical results, we construct approximate scheme to be used for producing numerical solutions of the considered fractional differential equation. As an illustrative numerical example, we consider two Riccati fractional differential equations with different derivatives: Atangana–Baleanu Caputo and Caputo derivatives. Finally, the study of those examples verifies the theoretical results of global existence and uniqueness of solution. Moreover, numerical results underline the difference between solutions of both examples.