Solution of fractional Laplace type equation in conformable sense using fractional fourier series with separation of variables technique
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Keywords:
Fractional Fourier series, conformable fractional derivative, atomic solutionAbstract
The fractional Fourier series method with the separation of variables technique has been applied to solve the fractional Laplace type equation. We use the conformable fractional derivative to study the fractional Laplace type equation and solve it using the conformable fractional Fourier series method with separation of variables and tensor product technique in Banach spaces.
References
Abdeljawad, T., On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, (2015), 57–66.
Khalil, R., Al-Horani, M., Yousef, A., and Sababheh, M., A New definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, (2014), 65–70.
Khalil, R., Isometries of L p* X L p . Tamkang Journal of Mathematics, 16 (2), (1985), 77–85.
Abu Hammad, M. A., and Khalil, R., Fractional Fourier series with applications. American Journal of Computational and Applied Mathematics, 4 (6), (2014), 187–191.
Cenesiz, Y., and Kurt, A., The solutions of time and space comformable fractional heat equations with conformable Fourier transform. Acta Universitatis Sapientiae, Mathematica, 7 (2), (2015), 130–140.
Podlubny, I., Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press,
Kadri, I., Horani, M., and Khalil, R., Tensor product technique and fractional differential equations. Journal of Semigroup Theory and Applications, 2020, (2020), Article-ID 6.
Khalil, R., and Abdullah, L., Atomic solution of certain inverse problems. European Journal of Pure and Applied Mathematics, 3 (4), (2010), 725–729.
Ilhem, K., Al Horani, M., and Khalil, R. R., Solution of Non-linear Fractional Burger’s type Equations using the Laplace Transform Decomposition Method. Results in Nonlinear Analysis, 5 (2), (2022), 131–151.
Light, W., and Cheney, E., Approximation Theory in Tensor Product Spaces, 1169, New York: Springer, (1985),