Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations

Parisa Rahimkhani and Mohammad Hossein Heydari

Chaos, Solitons & Fractals, 2023, vol. 175, issue P2

Abstract: We provide an effective numerical strategy for fractal-fractional pantograph differential equations (FFPDEs). The fractal-fractional derivative is considered in the Atangana–Riemann–Liouville sense. The scheme is based on fractional shifted Morgan-Voyce neural network (FShM-VNN). We introduce a new class of functions called fractional-order shifted Morgan-Voyce and some useful properties of these functions for the first time. The FShM-VNN method is utilized the fractional-order shifted Morgan-Voyce functions (FShM-VFs) and Sinh function as activation functions of the hidden layer and output layer of the neural network (NN), respectively. The approximate function contains the FShM-VFs with unknown weights. Using the classical optimization method and Newton’s iterative scheme, the weights are adjusted such that the approximate function satisfies the under study problem. Convergence analysis of the mentioned strategy is discussed. The scheme yields very accurate outcomes. The obtained numerical examples support this assertion.

Keywords: Fractal-fractional pantograph differential equations; Fractional-order shifted Morgan–Voyce functions; Neural networks; Error estimate (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077923009712
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923009712

DOI: 10.1016/j.chaos.2023.114070

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().