A novel neural network-based method for solving fractional differential equations involving the generalized Caputo operator
Abstract
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.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Advanced Control Systems Design
Neural Networks and Applications
Publication details
- Journal / source
- Advanced Studies Euro-Tbilisi Mathematical Journal
- Publisher
- Tbilisi Centre for Mathematical Sciences
- Volume
- 19
- Issue
- 1
- Pages
- 233-252
- Publication date
- 31 March 2026