Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network

Abstract

Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying fractional radial basis function neural network. The fractional derivative used in the method is considered Riemann-Liouville type. This method is simple to implement and approximates the solution of any arbitrary point inside or outside the domain after training the ANN model. Finally, three examples are presented to show the validity and applicability of the method.

Keywords

• artificial neural networks
• RBF
• radial basis function
• fractional differential equations
• fractional RBF
• initial value problems