Diamond Alpha Differentiability of Interval-Valued Functions and Its Applicability to Interval Differential Equations on Time Scales

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F24%3AA2502N65" target="_blank" >RIV/61988987:17310/24:A2502N65 - isvavai.cz</a>

Výsledek na webu

<a href="https://ijfs.usb.ac.ir/article_8073.html" target="_blank" >https://ijfs.usb.ac.ir/article_8073.html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.22111/IJFS.2024.45184.7977" target="_blank" >10.22111/IJFS.2024.45184.7977</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Diamond Alpha Differentiability of Interval-Valued Functions and Its Applicability to Interval Differential Equations on Time Scales

Popis výsledku v původním jazyce

Modelling phenomena with interval differential equations (IDEs) is an effective way to consider the uncertainties that are unavoidable when collecting data. Similarly to the theory of ordinary differential equations, IDEs have been parallelly investigated with the interval difference equations from the beginning. These two branches can be regarded as one when unifying continuous and discrete solution domains. A conspicuous advantage when merging these areas is that the proof of several analogous properties in both theories need not be repeated. The paper provides a common and efficient tool for studying IDEs not only with continuous or discrete solution domains but also with more general ones. We propose the diamond-$alpha$ derivative for interval-valued functions (IVFs) on time scales with respect to the generalized Hukuhara difference. Differently from most of the studies on the derivatives of functions on time scales, using the language of epsilon-delta, the novel concept is naturally studied according to the limit of IVFs on time scales as in classical mathematics. A particular class of IDEs on time scales is then considered with respect to the diamond-$alpha$ derivative. Numerical problems are elaborated to illustrate the necessity and efficiency of the latter.

Název v anglickém jazyce

Diamond Alpha Differentiability of Interval-Valued Functions and Its Applicability to Interval Differential Equations on Time Scales

Popis výsledku anglicky

Modelling phenomena with interval differential equations (IDEs) is an effective way to consider the uncertainties that are unavoidable when collecting data. Similarly to the theory of ordinary differential equations, IDEs have been parallelly investigated with the interval difference equations from the beginning. These two branches can be regarded as one when unifying continuous and discrete solution domains. A conspicuous advantage when merging these areas is that the proof of several analogous properties in both theories need not be repeated. The paper provides a common and efficient tool for studying IDEs not only with continuous or discrete solution domains but also with more general ones. We propose the diamond-$alpha$ derivative for interval-valued functions (IVFs) on time scales with respect to the generalized Hukuhara difference. Differently from most of the studies on the derivatives of functions on time scales, using the language of epsilon-delta, the novel concept is naturally studied according to the limit of IVFs on time scales as in classical mathematics. A particular class of IDEs on time scales is then considered with respect to the diamond-$alpha$ derivative. Numerical problems are elaborated to illustrate the necessity and efficiency of the latter.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Iranian Journal of Fuzzy Systems

ISSN

1735-0654

e-ISSN

2676-4334

Svazek periodika

—

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IR - Íránská islámská republika

Počet stran výsledku

15

Strana od-do

143-158

Kód UT WoS článku

001169497500001

EID výsledku v databázi Scopus

2-s2.0-85189501118