Complex-valued fractional derivatives on time scales
arXiv:1511.02153 · doi:10.1007/978-3-319-32857-7_8
Abstract
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
This is a preprint of a paper whose final and definite form will appear in Springer Proceedings in Mathematics & Statistics, ISSN: 2194-1009. Accepted for publication 06/Nov/2015
References in corpus (5)
- A Conformable Fractional Calculus on Arbitrary Time Scales
- A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
- Existence and Uniqueness of Solution for a Fractional Riemann-Liouville Initial Value Problem on Time Scales
- Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
- Generalized fractional operators for nonstandard Lagrangians
Cited by in corpus (8)
- Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
- Global stability of a Caputo fractional SIRS model with general incidence rate
- Generalized Fractional Operators on Time Scales with Application to Dynamic Equations
- Time-Fractional Optimal Control of Initial Value Problems on Time Scales
- Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
- A Truly Conformable Calculus on Time Scales
- The fuzzy Henstock-Kurzweil delta integral on time scales
- Structural derivatives on time scales