Conformable Derivatives in Laplace Equation and Fractional Fourier Series Solution

  • 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

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 < α ≤ 2 has been deduced by using fractional fourier series and separation of variables method. For special cases α =2 (Laplace's equation), α=1.9, and α=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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Published
2019-11-07
How to Cite
[1]
R. Pashaei, M. Asgari, and A. Pishkoo, “Conformable Derivatives in Laplace Equation and Fractional Fourier Series Solution”, Int. Ann. Sci., vol. 9, no. 1, pp. 1-7, Nov. 2019.
Section
Research Article