Geodesic
Analytical solution of the space-time fractional reaction--diffusion equation with~variable coefficients
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 3, pp. 430-444

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In this paper, we solve the problem of an inhomogeneous one-dimensional fractional differential reaction–diffusion equation with variable coefficients (1.1)–(1.2) by the method of separation of variables (the Fourier method). The Caputo derivative and the Riemann–Liouville derivative are considered in the time and space directions, respectively. We prove that the obtained solution of the boundary-value problem satisfies the given boundary conditions. We discuss the convergence of the series defining the proposed solution.
Mots-clés : reaction–diffusion equation, advective diffusion
Keywords: boundary-value problem, fractional derivative, Caputo derivative, Riemann–Liouville derivative, separation of variables method, Fourier method. 
@article{CMFD_2023_69_3_a3,
     author = {E. I. Mahmoud},
     title = {Analytical solution of the space-time fractional reaction--diffusion equation with~variable coefficients},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {430--444},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_3_a3/}
}
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E. I. Mahmoud. Analytical solution of the space-time fractional reaction--diffusion equation with~variable coefficients. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 3, pp. 430-444. http://geodesic.mathdoc.fr/item/CMFD_2023_69_3_a3/