Ardeshiri Lordejani, MaryamAfshar Kermani, MozhdehAllahviranloo, Tofigh2022-11-132022-11-132022Lordejani, M. A., Kermani, M. A., & Allahviranloo, T. (2022). Z+-Laplace transforms and Z+-differential equations of the arbitrary-order, theory and applications. Information Sciences.0020-0255https://doi.org/10.1016/j.ins.2022.10.047https://hdl.handle.net/20.500.12713/3373This 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.eninfo:eu-repo/semantics/closedAccessZ+-Laplace Transforms And Z+-Differential Equations Of The Arbitrary-OrderTheory And Applications Electric Circuit ModelRadioactive Decay Model; Z+-Differential EquationZ+-Laplace TransformArticle6176590WOS:0008808138000042-s2.0-85140962007Q110.1016/j.ins.2022.10.047Q1