Z+-laplace transforms and Z+-differential equations of the arbitrary-order, theory and applications

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dc.authoridTofigh Allahviranloo / 0000-0002-6673-3560en_US
dc.authorscopusidTofigh Allahviranloo / 8834494700en_US
dc.authorwosidTofigh Allahviranloo / V-4843-2019en_US
dc.contributor.authorArdeshiri Lordejani, Maryam
dc.contributor.authorAfshar Kermani, Mozhdeh
dc.contributor.authorAllahviranloo, Tofigh
dc.date.accessioned2022-11-13T19:27:43Z
dc.date.available2022-11-13T19:27:43Z
dc.date.issued2022en_US
dc.departmentİstinye Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractThis paper provides a framework to study a class of arbitrary-order uncertain differential equations known as arbitrary-order Z+-differential equations. For this purpose, we first present the parametric form of Z+-numbers. Then, we introduce the basic algebraic operations on Z+-numbers, including addition, scalar multiplication, and Hukuhara difference. Definitely, these operations lead us to define the Z+-valued function. Afterward, the limit and continuity concepts of a Z+-valued function are provided under the definition of a metric on the space of Z+-numbers. Furthermore, the concepts of Z+-differentiability, Z+-integral, and Z+-Laplace transform with the convergence theorem for the Z+-valued function and its nth-order derivatives are introduced in detail. Considering all these concepts, a Z+-differential equation (Z+DE) can be expressed in the form of a bimodal differential equation combining a fuzzy initial value problem (FIVP) and a random differential equation (RDE). To this end, we use a combination of “FIVP under strongly generalized Hukuhara differentiability (SGH-differentiability)” and “random differential equation under mean-square differentiability (ms-differentiability)” to define the nth-order differential equations with Z+-number initial values. Further, the existence and uniqueness of the Z+-differential equations are examined by presenting several theorems. Finally, the effectiveness of the approaches is illustrated by solving two examples.en_US
dc.identifier.citationLordejani, M. A., Kermani, M. A., & Allahviranloo, T. (2022). Z+-Laplace transforms and Z+-differential equations of the arbitrary-order, theory and applications. Information Sciences.en_US
dc.identifier.doi10.1016/j.ins.2022.10.047en_US
dc.identifier.endpage90en_US
dc.identifier.issn0020-0255en_US
dc.identifier.scopus2-s2.0-85140962007en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage65en_US
dc.identifier.urihttps://doi.org/10.1016/j.ins.2022.10.047
dc.identifier.urihttps://hdl.handle.net/20.500.12713/3373
dc.identifier.volume617en_US
dc.identifier.wosWOS:000880813800004en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorAllahviranloo, Tofigh
dc.language.isoenen_US
dc.publisherElsevier Inc.en_US
dc.relation.ispartofInformation Sciencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectZ+-Laplace Transforms And Z+-Differential Equations Of The Arbitrary-Orderen_US
dc.subjectTheory And Applications Electric Circuit Modelen_US
dc.subjectRadioactive Decay Model; Z+-Differential Equationen_US
dc.subjectZ+-Laplace Transformen_US
dc.titleZ+-laplace transforms and Z+-differential equations of the arbitrary-order, theory and applicationsen_US
dc.typeArticleen_US

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