Conformable Derivatives in Laplace Equation and Fractional Fourier Series Solution

Ronak Pashaei; Mohammad Sadegh Asgari; Amir Pishkoo

doi:10.21467/ias.9.1.1-7

Authors

Ronak Pashaei Islamic Azad University, Central Tehran Branch, Tehran
Mohammad Sadegh Asgari Islamic Azad University, Central Tehran Branch, Tehran
Amir Pishkoo Physics and Accelerators Research School, Nuclear Science and Technology Research Institute, Tehran

DOI:

https://doi.org/10.21467/ias.9.1.1-7

Abstract

In this paper the solution of conformable Laplace equation, \frac{\partial^{\alpha}u(x,y)}{\partial x^{\alpha}}+ \frac{\partial^{\alpha}u(x,y)}{\partial y^{\alpha}}=0, where 1 < Î± â‰¤ 2 has been deduced by using fractional fourier series and separation of variables method. For special cases Î± =2 (Laplace's equation), Î±=1.9, and Î±=1.8 conformable fractional fourier coefficients have been calculated. To calculate coefficients, integrals are of type "conformable fractional integral".

Keywords:

Fractional fourier series, Conformable fractional derivative, Fractional Laplace's equation

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References

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