In this paper, we get exact solution of the time-fractional advection-dispersion equation with reaction term, where the Caputo fractional derivative is considered of order α ϵ (0,2]. The solution is achieved by using a function transform, Fourier and Laplace transforms to get the formulas of the fundamental solution, which are expressed explicitly in terms of Fox’s H-function by making use of the relationship between Fourier and Mellin transforms. As special cases the exact solutions of time-fractional diffusion and wave equations are also obtained, and the solutions of the integer order equations are mentioned.
Salim, Tariq O. and El-Kahlout, Ahmad
Analytical Solution of Time-Fractional Advection Dispersion Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 4,
1, Article 14.
Available at: https://digitalcommons.pvamu.edu/aam/vol4/iss1/14