New definitions of exponential, hyperbolic and trigonometric functions on time scales

DOI10.1016/j.jmaa.2011.11.023zbMath1237.26019arXiv1003.0697OpenAlexW2159697785MaRDI QIDQ662045

Jan L. Cieśliński

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0697

zbMATH Keywords

exponential functionhyperbolic functionstrigonometric functionstime scalesCayley transformmeasure chainsexact discretizationfirst and second order dynamic equations

Mathematics Subject Classification ID

Dynamic equations on time scales or measure chains (34N05) Real analysis on time scales or measure chains (26E70)

Related Items (13)

On Burgers equation on a time-space scale ⋮ Relativity of arithmetic as a fundamental symmetry of physics ⋮ Exponentials and Laplace transforms on nonuniform time scales ⋮ Stability and stabilizability of linear time-delay systems on homogeneous time scales ⋮ Hyers-Ulam stability and best constant for Cayley \(h\)-difference equations ⋮ The sine-Gordon equation on time scales ⋮ Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems ⋮ Lax systems and nonlinear equations on a time-space scale ⋮ A multivalued logarithm on time scales ⋮ Variational approach to second-order impulsive dynamic equations on time scales ⋮ 3 soliton solution to Sine-Gordon equation on a space scale ⋮ A dynamic matrix exponential via a matrix cylinder transformation ⋮ A new approach to interval-valued inequalities

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