Search results for: Ahmet Yantır

Items from 1 to 6 out of 6 results

chapter

Mathematica Applications on Time Scales

Ahmet Yantır, Ünal Ufuktepe

Lecture Notes in Computer Science > Computational Science and Its Applications – ICCSA 2005 > Symbolic Computation, SC 2005 Workshop > 529-537

Stefan Hilger introduced the calculus on time scales in order to unify continuous and discrete analysis in 1988. The study of dynamic equations is an active area of research since time scales unifies both discrete and continuous processes, besides many others. In this paper we give many examples on derivative and integration on time scales calculus with Mathematica. We conclude with solving the first...

chapter

Measure on Time Scales with Mathematica

Ünal Ufuktepe, Ahmet Yantır

Lecture Notes in Computer Science > Computational Science – ICCS 2006 > Poster Session II > 916-919

In this paper we study the Lebesgue Δ-measure on time scales. We refer to [3, 4] for the main notions and facts from the general measure and Lebesgue Δ integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Δ- and Lebesgue $\nabla$ - measure on an arbitrary time scale and also on a discrete time scale whose rule is...

chapter

Basic Calculus on Time Scale with Mathematica

Ahmet Yantır, Ünal Ufuktepe

Lecture Notes in Computer Science > Computational Science — ICCS 2003 > Russian Track > 821-827

Mathematical modeling of time dependent systems are always interesting for applied mathematicians. First continuous and then discrete mathematical modeling are built during the mathematical development from ancient to the modern times. By the discovery of the time scales, the problem of irregular controlling of time dependent systems is solved in 1990’s. In this paper, we explain the derivative of...

article

On continuous dependence of solutions of dynamic equations

Mieczysław Cichoń, Ahmet Yantir

Applied Mathematics and Computation > 2015 > 252 > Complete > 473-483

The main goal of the paper is to present a new approach to the problem of continuous dependence of solutions of differential or dynamic problems on their domains. This is of particular interests when we use dynamic (difference, in particular) equations as discretization of a given one. We cover a standard construction based of difference approximations for the continuous one, but we are not restricted...

article

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Ahmet Yantir, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak

Open Mathematics > 2015 > 13 > 1

In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of...

article

Weak solutions for the dynamic Cauchy problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak, Ahmet Yantir

Nonlinear Analysis > 2009 > 71 > 7-8 > 2936-2943

This paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete Cauchy problem in Banach spaces. We offer the existence of the weak solution of dynamic Cauchy problem on an infinite time scale. The measure of weak noncompactness and the fixed point theorem of Kubiaczyk are used to prove the main result.

INFONA - science communication portal

Search results for: Ahmet Yantır

Mathematica Applications on Time Scales

Measure on Time Scales with Mathematica

Basic Calculus on Time Scale with Mathematica

On continuous dependence of solutions of dynamic equations

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Weak solutions for the dynamic Cauchy problem in Banach spaces

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INFONA - science communication portal

Search results for: Ahmet Yantır

Mathematica Applications on Time Scales

Measure on Time Scales with Mathematica

Basic Calculus on Time Scale with Mathematica

On continuous dependence of solutions of dynamic equations

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Weak solutions for the dynamic Cauchy problem in Banach spaces

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