Abstract
We propose a generalization of conformable calculus for Type-2 interval-valued functions. We investigated the differentiability and integrability properties of such functions. The conformable generalized Hukuhara (gH) differentiability of fractional order is introduced in this study. We prove a number of essential theorems on the conformable differentiability of the sum, gH difference, and product in a Type 2 interval setting. Furthermore, we define conformable Laplace transformation of Type-2 interval-valued functions. We interpret uncertain linear differential equations by using proposed theories. Several examples are given in detail to illustrate and clarify these rules and theorems. Applications to solving Type-2 interval differential equations with conformable derivatives are shown. Type-2 interval generalizes the interval uncertainty. On the other hand, conformable calculus extends the notion of integer calculus. This paper contributes a generalized theory that includes several existing results of classical integral and differential calculus and their conformable extensions in crisp and interval environments.
•The notion of fractional conformable differentiation is extended in the new interval environment.•A new version fractional Laplace transform is developed.•The theory has been validated by several examples.