**Numerical Simulation Using Artificial Neural Network on Fractional Differential Equations**

Najeeb Alam Khan, Amber Shaikh, Faqiha Sultan and Asmat Ara

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64151

#### **Abstract**

This chapter offers a numerical simulation of fractional differential equations by utilizing Chebyshev-simulated annealing neural network (ChSANN) and Legendre-simulated annealing neural network (LSANN). The use of Chebyshev and Legendre polynomials with simulated annealing reduces the mean square error and leads to more accurate numerical approximation. The comparison of proposed methods with previous methods confirms the accuracy of ChSANN and LSANN.

**Keywords:** neural network, fractional Riccati, Legendre polynomial, Chebyshev poly‐ nomial, simulated annealing
