253 citations · 640 across the 9 of their papers we have counts for
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math.CA2012★ 12 cited
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…
math.CA2010★ 41 cited
Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform
Nuno R. O. Bastos, Dorota Mozyrska, Delfim F. M. Torres
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order deriva…
math.CA2010★ 12 cited
Combined Delta-Nabla Sum Operator in Discrete Fractional Calculus
Nuno R. O. Bastos, Delfim F. M. Torres
We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional op…