**5. Conclusion**

In this chapter, ChSANN and LSANN have been developed for fractional differential equa‐ tions and successfully employed on two benchmark examples of Riccati differential equations. The proposed methods gave the excellent numerical approximation of the Riccati differential equation of fractional order. The most remarkable advantage of the proposed methods is the accurate prediction of the result for the fractional values of derivative. These procedures are easy to implement and can be used to find the exact solution in the fractional values of derivative. ChSANN displayed more accurate results than LSANN for the similar applied conditions. Both the proposed algorithms are non-iterative and can be implemented through mathematical software and Mathematica 10 was used in this study to obtain all the results displayed in **Tables 1**–**10** and **Figures 2**–**4**.
