An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels. (March 2020)

• Record Type: Journal Article
• Authors: Heydari, M. H.; Atangana, A.
• Is Part Of: Chaos, solitons and fractals. Volume 132(2020)
• Publication Date: 2020-03
• Subjects: Mobile-immobile advection-dispersion equation -- Optimization scheme -- Generalized Lucas polynomials (GLPs) -- Operational matrices; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109588
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: A new version of variable-order (VO) space-time mobile-immobile advectiondispersion equation is introduced. The V-O fractional derivatives are defined in the Atangana-Baleanu-Caputo sense with Mittag-Leffler non-singular kernel. Some new operational matrices of V-O fractional derivatives are elicited for the generalized Lucas polynomials (GLPs). An optimization method based on the GLPs is proposed for the numerical solution of this class of problems. The applicability and accuracy of the proposed approach are demonstrated by solving some numerical examples. The proposed method can be extended for other types of V-O fractional problems. Abstract: This paper introduces a novel version of variable-order (VO) space-time mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels. An optimization scheme is proposed for solving this new class of VO fractional problems.The presented method is based on the hybrid of the generalized Lucas polynomials together with their operational matrices of VO fractional derivatives (which are obtained for the first time in the presented study), the collocation technique and the Lagrange multipliers scheme. The presented method transforms obtaining the solution of such problems into obtaining the solution of systems of algebraic equations. Two numerical examples are provided to show the validity and accuracy of the presented approach.