The Structure of Fractional Spaces Generated by a Two-dimensional Difference Operator in a Half Plane
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DOI: 10.1007/s11253-018-1561-5
Abstract: We consider a difference-operator approximation Ahx$$ {A}_h^x $$ of the differential operatorAxux=−a11xux1x1x−a22xux2x2x+σux,x=x1x2,$$ {A}^xu(x)=-{a}_{11}(x){u}_{x_1{x}_1}(x)-{a}_{22}(x){u}_{x_2{x}_2}(x)+\sigma u(x),\kern1em x=\left({x}_1,{x}_2\right), $$defined in the region ℝ+ × ℝ with the boundary condition u0x2=0,x2∈ℝ.$$ u\left(0,{x}_2\right)=0,\kern1em {x}_2\in \mathbb{R}. $$ Here, the coefficients aii(x),… read more here.
Keywords: difference; difference operator; spaces generated; structure fractional ... See more keywords