A novel neural network-based method for solving fractional differential equations involving the generalized Caputo operator

A. Antony, L. N. Mishra

In order to solve generalized Caputo-type fractional differential equations for both intact and broken-down systems, this paper introduces a unique neural network-based method. A novel framework is created by combining functional connection techniques with physics-based neural networks and extreme learning machines. In the proposed method, a loss function is constructed by the B-spline method utilizing the Volterra integral equation and the L1 finite scheme. In order to address generalized Caputo-type fractional differential equations, this study presents a novel neural network-based approach that combines functional connection theory with a novel loss function. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 233-252