A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation. (November 2020)

• Record Type: Journal Article
• Authors: Heydari, M.H.; Hosseininia, M.; Atangana, A.; Avazzadeh, Z.
• Is Part Of: Engineering analysis with boundary elements. Volume 120(2020)
• Page Start: 166
• Page End: 179
• Publication Date: 2020-11
• Subjects: Moving least squares (MLS) method -- 2D Ginzburg-Landau equation -- Variable-order (VO) fractional derivative; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.08.015
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper introduces the nonlinear variable-order (VO) time fractional 2D Ginzburg-Landau equation by replacing the conventional derivative with the Atangana–Baleanu–Caputo fractional derivative. An efficient moving least squares (MLS) meshfree approximation method is considered to devise an algorithm for solving this enhanced equation. To be precise, first, the finite difference scheme is used to evaluate the fractional differentiation. Then, a recurrence formula is derived by applying the θ -weighted technique. Next, the real and imaginary components of the solution are expanded in terms of meshless functions. Last, these expansions which include unknown coefficients are input in the original equation. Therefore, the equation is converted into a system of linear algebraic equations which is uncomplicated for solving by mathematical software. To verify the validity of the devised method and demonstrate its precision, several problems are put to the test.