The Novel Mittag-Leffler–Galerkin Method: Application to a Riccati Differential Equation of Fractional Order

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called Mittag-Leffler–Galerkin method—comprises finite Mittag-Leffler function and Galerkin method. error analysis of method was studied. As result, we two theorems by which can be bounded. In addition analysis, residual correction method, allows us estimate obtain approximate solutions, is also presented. To show how applied, efficiency proposed some test examples were considered. When results obtained examined, it found that while achieves better than known methods in literature, are similar those others methods.