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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Iranian Journal of Fuzzy Systems

ISSN

1735-0654

e-ISSN

2676-4334

Volume of the periodical

—

Issue of the periodical within the volume

1

Country of publishing house

IR - IRAN, ISLAMIC REPUBLIC OF

Number of pages

15

Pages from-to

143-158

UT code for WoS article

001169497500001

EID of the result in the Scopus database

2-s2.0-85189501118