Dynamic equations (…) on time scales

By Aneta Sikorska-Nowak. 2011

542 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/53e77c2fbedd45600752effde3cea740bb81c019

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1. Ferhan Merdivenci Atici
2. Paul W. Eloe
3. Christopher S. Goodrich
4. Delfim F. M. Torres
5. John M. Davis
6. Natália Martins
7. Jeffrey J. Dacunha
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Citations in the corpus

• Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions (2015, unknown): “Before describing the studied class of systems, let us recall some basic notations, definitions and properties of this theory [1].”
• Linear impulsive dynamic systems on time scales (2010, background): “([15]) If A, B : T → Mn(R) are differentiable, then (i) A(t) = A(t) + μ(t)A(t) for all t ∈ T; (ii) (A ) = (A) ; (iii) (A + B) = A + B, and (AB) = AB + AB = AB + AB; (iv) (A) = −(A)AA = −AA(A)if AA is invertible; (v) (AB) = (A − ABB)(B) = [A − (AB)B]B if BB is invertible.”
• EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES (2010, background): “It is evident from various papers (see [1, 5, 6, 12] and references therein) that dynamic equations on time scales are useful tools to explain the differences and similarities between difference and differential equations.”
• Two-point boundary value problems for finite fractional difference equations (2011, methodology): “We point out that we shall employ throughout the notation, sðsÞ, because eventually progress will be made to develop the theory of fractional calculus on time scales [6].”
• Calculus of variations on time scales with nabla derivatives (2008, methodology): “Introduction The theory oftime scaleswas born in 1988 with the work of Stephan Hilger [12], providi ng a rich theory that unify and extend discrete and continuous a nalysis [6, 7].”
• A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems (2009, background): “An excellent introduction to the subject of time scales analysis can be found in Bohner and Peterson’s introductory texts [5, 6].”