253 citations · 640 across the 9 of their papers we have counts for
10 papers
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…
A numerical method to solve higher-order fractional differential equations
Ricardo Almeida, Nuno R. O. Bastos
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation form…
An approximation formula for the Katugampola integral
Ricardo Almeida, Nuno R. O. Bastos
The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type…
Modelling some real phenomena by fractional differential equations
Ricardo Almeida, Nuno R. O. Bastos, M. Teresa T. Monteiro
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experi…
A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives
Ricardo Almeida, Nuno R. O. Bastos, Delfim F. M. Torres
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional op…
Fractional Calculus on Time Scales
Nuno R. O. Bastos
We introduce a discrete-time fractional calculus of variations on the time scales and . First and second order necessary optimality conditions are est…