A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
arXiv:1405.2813 · doi:10.1016/j.sigpro.2014.05.026
Abstract
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 (fractional differentiation and fractional integration) are then developed. As particular cases, one obtains the usual time-scale Hilger derivative when the order of differentiation is one, and a local approach to fractional calculus when the time scale is chosen to be the set of real numbers.
arXiv commentThis is a preprint of a paper whose final and definite form will appear in the international journal Signal Processing, ISSN 0165-1684. Paper submitted 04/Jan/2014; revised 19/Apr/2014; accepted for publication 12/May/2014
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- Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales
- Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
- Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
- Generalized Fractional Operators on Time Scales with Application to Dynamic Equations
- Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences
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- Time-Fractional Optimal Control of Initial Value Problems on Time Scales
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- Analysis of fractional integro-differential equations of thermistor type
- Noether's currents for conformable fractional scalar field theories
- The fuzzy Henstock-Kurzweil delta integral on time scales