Abstract—This paper investigates the problem of a fractional differential equation with moving concentrated source in an infinite rod. This fractional differential operator is used to formulate the diffusion problem in a subdiffusive medium. The existence of the solution is established, the finite time blow-up criteria for the solution of the problem is given. The critical speed of the concentrated sources on the behavior of the solution is investigated.

Index Terms—Green’s function, fractional diffusion equations, fractional derivatives, moving concentrated source.

H. T. Liu is with Department of Information Management, Tatung University, Taipei, Taiwan.

Cite:H. T. Liu, "Existence of the Solution for the Problem in Subdiffusive Medium with a Moving Concentrated Source ," International Journal of Applied Physics and Mathematics vol. 11, no. 4, pp. 71-77, 2021.

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