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**Solving fractional advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative.**
*(English)*
Zbl 1473.35635

Summary: 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.

### MSC:

35R11 | Fractional partial differential equations |

35A35 | Theoretical approximation in context of PDEs |

35K15 | Initial value problems for second-order parabolic equations |

### Keywords:

Atangana-Baleanu derivative; Atangana-Baleanu integral; advection-diffusion equation; operational matrix; Genocchi polynomials
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\textit{S. Sadeghi} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 10, 3747--3761 (2021; Zbl 1473.35635)

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### References:

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