A new artificial neural network structure for solving high-order linear fractional differential equations

ABSTRACT

Artificial neural networks afford great potential in learning and stability against small perturbations of input data. Using artificial intelligence techniques and modelling tools offers an ever-greater number of practical applications. In the present study, an iterative algorithm, which was based on the combination of a power series method and a neural network approach, was used to approximate a solution for high-order linear and ordinary differential equations. First, a suitable truncated series of the solution functions were substituted into the algorithm's equation. The problem considered here had a solution as a series expansion of an unknown function, and the proper implementation of an appropriate neural architecture led to an estimate of the unknown series coefficients. To prove the applicability of the concept, some illustrative examples were provided to demonstrate the precision and effectiveness of this method. Comparing the proposed methodology with other available traditional techniques showed that the present approach was highly accurate.

KEYWORDS:

• High-order fractional differential equation
• power-series method
• artificial neural network
• criterion function
• back-propagation learning algorithm

2010 AMS SUBJECT CLASSIFICATION:

• 47H30

Disclosure statement

No potential conflict of interest was reported by the authors.