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math.NA2016
Caputo-Hadamard fractional derivatives of variable order
Ricardo Almeida
In this paper we present three types of Caputo-Hadamard derivatives of variable fractional order, and study the relations between them. An approximation formula for each fractional…
math.NA2016
A discretization of the Hadamard fractional derivative
Ricardo Almeida, Nuno R. O. Bastos
We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a…
math.NA2016
Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems
Ricardo Almeida, Agnieszka B. Malinowska, M. Luísa Morgado +1
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. T…