Artificial Neural Network Approach for Solving Fractional order initial value problems

Abstract

In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better describe sometimes various real world application problems of physical systems. Here we have employed multi-layer feed forward neural architecture and error back propagation algorithm with unsupervised learning for minimizing the error function and modification of the parameters (weights and biases). Combining the initial conditions with the ANN output gives us a suitable approximate solution of FDE. To prove the applicability of the concept, some illustrative examples are provided to demonstrate the precision and effectiveness of this method. Comparison of the present results with other available results by traditional methods shows a close match which establishes its correctness and accuracy of this method.