253 citations · 640 across the 9 of their papers we have counts for
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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…
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…
Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations
Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Eul…
Discrete-Time Fractional Variational Problems
Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres
We introduce a discrete-time fractional calculus of variations on the time scale , . First and second order necessary optimality conditions are established. Exa…