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

Autor:	Hassani, Hossein, Avazzadeh, Zakieh, Agarwal, Praveen, Ebadi, Mohammad Javad, Bayati Eshkaftaki, Ali
Předmět:	NONLINEAR systems PARTIAL differential equations ALGEBRAIC equations FRACTIONAL differential equations POLYNOMIALS LAGRANGE multiplier CHEBYSHEV polynomials
Zdroj:	Journal of Optimization Theory & Applications; Jan2024, Vol. 200 Issue 1, p371-393, 23p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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