Fractional Chebyshev deep neural network (FCDNN) for solving differential models

Zeinab Hajimohammadi, Fatemeh Baharifard, Ali Ghodsi and Kourosh Parand

Chaos, Solitons & Fractals, 2021, vol. 153, issue P2

Abstract: Differential and integral equations have been used vastly in modeling engineering and science problems. Solving these equations has been always an active and important area of research. In this paper, we propose the Fractional Chebyshev Deep Neural Network (FCDNN) for solving fractional differential models. Chebyshev orthogonal polynomials are basic functions in spectral methods. These functions are used as activation functions in FCDNN. The marching in time technique and the Gaussian method are applied in the fractional operations to simplify the calculations. We show how FCDNN can be used to solve fractional Fredholm integral equations (FFIEs). We also propose a solution to the extension of fractional time order partial differential equations (FPDEs). In this approach, fractional PDEs are first discretized by the finite difference and the marching in time methods and then are solved using FCDNN. Fractional Fredholm integral equations are also first approximated by the numerically Gaussian quadrature method and then are solved using FCDNN. A comparison between the results from FCDNN and some other methods is presented to validate the effectiveness and advance of the proposed method.

Keywords: Deep neural network; Chebyshev polynomials; Collocation method; Fractional partial differential equations (FPDEs); Fractional Fredholm integral equations (FFIEs) (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077921008845
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:153:y:2021:i:p2:s0960077921008845

DOI: 10.1016/j.chaos.2021.111530

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. ().