Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs

Hossein Hassani (), Zakieh Avazzadeh (), Praveen Agarwal (), Mohammad Javad Ebadi () and Ali Bayati Eshkaftaki ()
Additional contact information
Hossein Hassani: Anand International College of Engineering
Zakieh Avazzadeh: University of South Africa
Praveen Agarwal: Anand International College of Engineering
Mohammad Javad Ebadi: Chabahar Maritime University
Ali Bayati Eshkaftaki: Shahrekord University

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 1, No 13, 393 pages

Abstract: Abstract In this paper, we introduce a general class of coupled nonlinear systems of variable-order fractional partial differential equations (GCNSV-FPDEs) with initial and boundary conditions. We propose a hybrid method based on new generalized Bernoulli–Laguerre polynomials (GB-LPs) for solving GCNSV-FPDEs. The concept of variable-order fractional derivatives (V-FDs) is employed in the Caputo type. We extract the operational matrices (OMs) of classical and V-FDs of GB-LPs. By utilizing GB-LPs, OMs, and the Lagrange multipliers method, we transform the given GCNSV-FPDE into a system of algebraic equations to be solved. The proposed method yields satisfactory results even with a small number of GB-LPs. We provide a full verification of the method’s convergence, and two examples are included to demonstrate its validity and applicability.

Keywords: Coupled nonlinear system of variable-order fractional partial differential equation; Control parameters; Optimization; Generalized Bernoulli–Laguerre polynomials; 35C10; 35G61; 35R11 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-023-02346-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02346-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-023-02346-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().