A highly accurate artificial neural networks scheme for solving higher multi-order fractal-fractional differential equations based on generalized Caputo derivative

Abstract

Artificial neural networks have great potential for learning and stability in the face of tiny input data changes. As a result, artificial intelligence techniques and modeling tools have a growing variety of applications. To estimate a solution for fractal-fractional differential equations (FFDEs) of high-order linear (HOL) with variable coefficients, an iterative methodology based on a mix of a power series method and a neural network approach was applied in this study. In the algorithm's equation, an appropriate truncated series of the solution functions was replaced. To tackle the issue, this study uses a series expansion of an unidentified function, where this function is approximated using a neural architecture. Some examples were presented to illustrate the efficiency and usefulness of this technique to prove the concept's applicability. The proposed methodology was found to be very accurate when compared to other available traditional procedures. To determine the approximate solution to FFDEs-HOL, the suggested technique is simple, highly efficient, and resilient. © 2023 Elsevier B.V., All rights reserved.