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Title
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Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative
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Type
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JournalPaper
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Keywords
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Atangana-Baleanu derivative, Atangana-Baleanu integral, Advection-Diffusion equation, Operational matrix, Genocchi polynomials
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Abstract
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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.
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Researchers
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Somayeh Nemati (Third Researcher), Hossein Jafari (Second Researcher), sedigheh Sadeghi (First Researcher)
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