Directional Derivative of the Vector Field and Regular Curves on Time Scales

Emin Özyilmaz

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(10): 1182-1192

Emin Özyilmaz. Directional Derivative of the Vector Field and Regular Curves on Time Scales[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1182-1192.

Citation:

Emin Özyilmaz. Directional Derivative of the Vector Field and Regular Curves on Time Scales[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1182-1192.

Citation:

Emin Özyilmaz. Directional Derivative of the Vector Field and Regular Curves on Time Scales[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1182-1192.

PDF( 429 KB)

Directional Derivative of the Vector Field and Regular Curves on Time Scales

Emin Özyilmaz

Department of Mathematics, Ege University, 35100, ?zmir, Turkey

Received Date: 2005-08-01
Rev Recd Date: 2006-04-18
Publish Date: 2006-10-15

Abstract

Abstract

The general idea is to study curves where in the parametric equations the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. The directional derivative according to the vector fields was introduced.
- time scale,
- nabla derivative,
- regular curve,
- tangent line,
- vector field

FullText(HTML)

References(5)

References

[1]	Aulbach B，Hilger S. Linear dynamic processes with inhomogeneous time scale[A].In:Nonlinear Dynamics and Quantum Dynamical Systems[C].Berlin:Akademie Verlag,1990,9—20.
[2]	Ahlbrandt C D, Bohner M, Ridenhour J. Hamiltonian systems on time scales[J].J Math Anal Appl,2000，250：561—578. doi: 10.1006/jmaa.2000.6992
[3]	Hoffacker J. Basic partial dynamic equations on time scales[J].J Difference Equ Appl,2002,8(4):307—319.(In honor of Professor Lynn Erbe) doi: 10.1080/1026190290017379
[4]	Bohner M,Peterson A.Dynamic Equations on Time Scales—An Introduction With Applications[M].Boston: Birkhauser, 2001.
[5]	Bohner M, Guseinov G. Partial differentiation on time scales[J].Dynamic Systems and Applications,2003,12:351—379.