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In recent literature, for modeling reasons, fractional differential problemshave been considered equipped with anti-symmetric boundary conditions. Twentyyears ago the anti-reflective boundary conditions were introduced in a contextof signal processing and imaging for increasing the quality of thereconstruction of a blurred signal/image contaminated by noise and for reducingthe overall complexity to that of few fast sine transforms i.e. to $O(N\log N)$real arithmetic operations, where $N$ is the number of pixels. Here we considerthe anti-symmetric boundary conditions and we introduce the anti-reflectiveboundary conditions in the context of nonlocal problems of fractionaldifferential type. In the latter context, we study both types of boundaryconditions, which in reality are similar in the essentials, from theperspective of computational efficiency, by considering nontruncated andtruncated versions. Several numerical tests, tables, and visualizations areprovided and critically discussed.

Nonlocal problems with anti-symmetric and anti-reflective boundary conditions: a computational analysis and numerical comparisons