Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-018-0869-5
Abstract: This paper develops a Galerkin approach for two-sided fractional differential equations with variable coefficients. By the product rule, we transform the problem into an equivalent formulation which additionally introduces the fractional low-order term. We prove… read more here.
Keywords: two sided; galerkin approach; equations variable; sided fractional ... See more keywords
A-posteriori error estimations based on postprocessing technique for two-sided fractional differential equations
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.04.019
Abstract: Abstract The analysis of diffusion-reaction equations with general two-sided fractional derivative characterized by a parameter p ∈ [ 0 , 1 ] is investigated in this paper. First, we present a Petrov-Galerkin method, derive a… read more here.
Keywords: posteriori error; postprocessing technique; two sided; error ... See more keywords
On the regularity of one-sided fractional maximal functions
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DOI: 10.1515/ms-2017-0171
Abstract: Abstract In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators ℳβ+$ \mathcal{M}_{\beta}^{+} $ and ℳβ-$… read more here.
Keywords: maximal functions; one sided; mathbb mathbb; sided fractional ... See more keywords