204 citations · 374 across the 4 of their papers we have counts for
4 papers
Existence and Uniqueness of Solution for a Fractional Riemann-Liouville Initial Value Problem on Time Scales
Nadia Benkhettou, Ahmed Hammoudi, Delfim F. M. Torres
We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness…
A Conformable Fractional Calculus on Arbitrary Time Scales
Nadia Benkhettou, Salima Hassani, Delfim F. M. Torres
A conformable time-scale fractional calculus of order is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The…
Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
Nadia Benkhettou, Artur M. C. Brito da Cruz, Delfim F. M. Torres
We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentia…
A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
Nadia Benkhettou, Artur M. C. Brito da Cruz, Delfim F. M. Torres
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fraction…