FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS

By Rui A. C. Ferreira, Delfim F. M. Torres. 2011

180 citations recorded by the source corpus.

The recent theory of fractional h-difference equations introduced in [N.R.O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513{524], is enriched with useful tools for the explicit solution of discrete equations involving left and right fractional difference operators. New results for the right fractional h sum are proved. Illustrative examples show the effectiveness of the obtained results in solving fractional discrete Euler{Lagrange equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/8da8fb12c5d3e488fc314d3916beb2b0fe69d1cb

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In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

Comparison theorems and asymptotic behavior of solutions of discrete fractional equations (2015, background): “backward or nabla difference operator and we refer the readers to [5,7].”
Two monotonicity results for nabla and delta fractional differences (2015, background): “It seems, however, that more work has been developed for the backward or nabla difference operator, and we refer the readers to [5,8].”
Systems of semipositone discrete fractional boundary value problems (2014, background): “, [24]), the fractional calculus on different time scales (e.”
The -Transform Method and Delta Type Fractional Difference Operators (2015, methodology): “For a function x : (hN) a → R the forward h-difference operator is defined as (Δ h x)(t) := (x(σ(t))−x(t))/h, where t ∈ (hN) a , see [21, 22].”