Results 21 to 30 of about 247 (76)

A unified approach to the calculus of variations on time scales

, 2010
In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing the composition
Girejko, Ewa, Malinowska, Agnieszka B., Torres, Delfim F. M.   +2 more
core   +1 more source

Wiman’s formula for a second order dynamic equation [PDF]

, 2014
We derive Wiman’s asymptotic formula for the number of generalized zeros of (nontrivial) solutions of a second order dynamic equation on a time scale. The proof is based on the asymptotic representation of solutions via exponential functions on a time ...
Alan Peterson, Gro Hovhannisyan, Lynn Erbe   +2 more
core   +2 more sources

Sturm-Liouville operators on time scales

, 2011
We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have ...
Atkinson F., Davidson F.A., Erbe L., Gerald Teschl, Guseinov G.S., Guseinov G.S., Huseynov A., Huseynov A., Jonathan Eckhardt, Mingarelli A.B., Sun S., Teschl G., Volkmer H., Zhang C., Šimon Hilscher R.   +14 more
core   +4 more sources

Three-point boundary value problems with delta Riemann-Liouville fractional derivative on time scales [PDF]

, 2016
In this paper, we establish the criteria for the existence and uniqueness of solutions of a three-point boundary value problem for a class of fractional differential equations on time scales.
Liceli, Onur, Yaslan, İsmail
core   +1 more source

Converses of nabla Pachpatte-type dynamic inequalities on arbitrary time scales

Demonstratio Mathematica
Reverse Pachpatte-type inequalities are concave generalizations of the well-known Bennett-Leindler-type inequalities. We establish reverse nabla Pachpatte-type dynamic inequalities taking account of concavity.
Kayar Zeynep, Kaymakçalan Billur
doaj   +1 more source

Well-posedness and maximum principles for lattice reaction-diffusion equations

Advances in Nonlinear Analysis, 2017
Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations.
Slavík Antonín, Stehlík Petr, Volek Jonáš   +2 more
doaj   +1 more source

Delta-Nabla Optimal Control Problems

, 2010
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results ...
Agnieszka B Malinowska, Aulbach B., Bohner M., Delfim FM Torres, Ewa Girejko, Girejko E., Malinowska AB, Malinowska AB   +7 more
core   +1 more source

Some special functions and cylindrical diffusion equation on α-time scale

Demonstratio Mathematica
This article is dedicated to present various concepts on α\alpha -time scale, including power series, Taylor series, binomial series, exponential function, gamma function, and Bessel functions of the first kind.
Silindir Burcu, Tuncer Zehra, Gergün Seçil, Yantir Ahmet   +3 more
doaj   +1 more source

Avoidance Control on Time Scales

, 2009
We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions.
A. Bressan, A. Cabada, A. Cabada, A.F. Filippov, A.N. Kolmogorov, B.R. Barmish, D. F. M. Torres, E. Pawłuszewicz, E.D. Sontag, G. Leitmann, G. Leitmann, G. Leitmann, J.J. DaCunha, M. Bohner, M. Bohner, M. Corless, M. Corless, R. Aggarwal, R.P. Agarwal, Z. Bartosiewicz   +19 more
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Some Hardy's inequalities on conformable fractional calculus

Demonstratio Mathematica
In this article, we will demonstrate some Hardy’s inequalities by utilizing Hölder inequality, integration by parts, and chain rule of the conformable fractional calculus.
AlNemer Ghada, Saker Samir H., Ashry Gehad M., Zakarya Mohammed, Rezk Haytham M., Kenawy Mohammed R.   +5 more
doaj   +1 more source