Open AccessSolving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative
Author(s) -
S. Sadeghi,
Hossein Jafari,
Somayeh Nemati
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020435
Subject(s) - mathematics , bivariate analysis , derivative (finance) , matrix (chemical analysis) , diffusion , fractional calculus , kernel (algebra) , advection , function (biology) , mathematical analysis , pure mathematics , statistics , thermodynamics , materials science , physics , evolutionary biology , biology , financial economics , economics , composite material
In recent years, a new definition of fractional derivative which has a nonlocal and non-singular kernel has been proposed by Atangana and Baleanu. This new definition is called the Atangana-Baleanu derivative. In this paper, we present a new technique to obtain the numerical solution of advection-diffusion equation containing Atangana-Baleanu derivative. For this purpose, we use the operational matrix of fractional integral based on Genocchi polynomials. An error bound is given for the approximation of a bivariate function using Genocchi polynomials. Finally, some examples are given to illustrate the applicability and efficiency of the proposed method.