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A numerical approach based on ln‐shifted Legendre polynomials for solving a fractional model of pollution
Author(s) -
Jleli M.,
Kirane M.,
Samet B.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4534
Subject(s) - legendre polynomials , mathematics , discretization , hadamard transform , legendre's equation , fractional calculus , numerical analysis , mathematical analysis
The model of pollution for a system of 3 lakes interconnected by channels is extended using Caputo‐Hadamard fractional derivatives of different orders α i ∈(0,1), i =1,2,3. A numerical approach based on ln‐shifted Legendre polynomials is proposed to solve the considered fractional model. No discretization is needed in our approach. Some numerical experiments are provided to illustrate the presented method.