Abstract
This paper is devoted to developing the regularity results of the true (classic) solution to the homogeneous BVP of double-sided fractional diffusion advection reaction equation with variable coefficients on the bounded interval. This topic has been controversial in modelling in recent years, especially on the regularity issue. We use a different strategy of raising regularity of the weak solution and prove that, under suitable conditions, the true solution exists and can be represented in the form of fractional integration; furthermore, we show that usually this integral representation cannot be further improved even with smooth coefficients and right-hand side function in the equation. And we find the precise bound for this integral representation to hold, which measures the “best” regularity guaranteed and is in sharp contrast to the case of integer-order elliptic PDEs.
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