Solvability Criteria for Uncertain Differential Equations and Their Applicability in an Economic Lot-Size Model with a Type-2 Interval Phenomenon

Abstract

Interval numbers comprise potential fields of application and describe the imprecision brought on by the flexible nature of data between boundaries. The recently added type-2 interval number allows a more thorough understanding of interval numbers. Differential equations are commonly employed in mathematical models to handle dynamic problems. It is essential to provide theories of differential equations to describe these models in an ambiguous environment controlled by type-2 interval numbers. This study proposes the type-2 interval context solvability requirements for the initial-valued first differential equation. The conditions for the solution’s existence and uniqueness must be met before a brief manifestation of the solution under generalized Hukuhara differentiation occurs. An economic order quantity model analysis in a type-2 interval scenario uses a generalized Hukuhara differentiation approach.

Keywords

• generalized Hukuhara difference
• type-2 interval number
• generalized Hukuhara differentiability
• Riemann integrability
• differential equation
• existence and uniqueness theorem