The maximal \(B_{p,q}^{s}\)-regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in \( B_{p,q}^{s}\) and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces is obtained. Then by using the \(B_{p,q}^{s}\)-regularity properties of linear problem, the existence, uniqueness of maximal regular solution of corresponding fractional nonlinear equation is established.

中文翻译：

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Besov 空间中分数卷积椭圆和抛物线算子的定性性质

研究了分数阶卷积椭圆方程的最大\(B_{p,q}^{s}\)正则性性质。特别地，证明了该非局部椭圆方程生成的算子在\(B_{p,q}^{s}\)中是扇形的，并且是一个解析半群的生成元。此外，还得到了Besov空间中非局部分数式抛物型方程的适定性。然后利用线性问题的\(B_{p,q}^{s}\)正则性性质，建立相应分数阶非线性方程最大正则解的存在唯一性。