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We present a novel definition of variable-order fractional Laplacian on $${\mathbb {R}}^n$$ R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of… Click to show full abstract
We present a novel definition of variable-order fractional Laplacian on $${\mathbb {R}}^n$$ R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n /2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.
Keywords:
variable order;
order fractional;
fractional laplacian;
laplacian variable
Journal Title: Fractional Calculus and Applied Analysis
Year Published: 2022
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Journal Title: Fractional Calculus and Applied Analysis
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!