9 research outputs found
Time-Fractional Optimal Control of Initial Value Problems on Time Scales
We investigate Optimal Control Problems (OCP) for fractional systems
involving fractional-time derivatives on time scales. The fractional-time
derivatives and integrals are considered, on time scales, in the
Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient
conditions for existence and uniqueness of solution to initial value problems
described by fractional order differential equations on time scales are known.
Here we consider a fractional OCP with a performance index given as a
delta-integral function of both state and control variables, with time evolving
on an arbitrarily given time scale. Interpreting the Euler--Lagrange first
order optimality condition with an adjoint problem, defined by means of right
Riemann--Liouville fractional delta derivatives, we obtain an optimality system
for the considered fractional OCP. For that, we first prove new fractional
integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book
chapter with Springer International Publishing AG. Submitted 23/Jan/2019;
revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial
text overlap with arXiv:1508.0075
Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
We introduce new fractional operators of variable order on isolated time
scales with Mittag-Leffler kernels. This allows a general formulation of a
class of fractional variational problems involving variable-order difference
operators. Main results give fractional integration by parts formulas and
necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with
Springe
The fuzzy Henstock–Kurzweil delta integral on time scales
We investigate properties of the fuzzy Henstock–Kurzweil delta integral (shortly, FHK Δ -integral) on time scales, and obtain two necessary and sufficient conditions for FHK Δ -integrability. The concept of uniformly FHK Δ -integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK Δ -integral.publishe