Fractional Calculus for Type 2 Interval-Valued Functions

Abstract

This paper presents a contemporary introduction of fractional calculus for Type 2 interval-valued functions. Type 2 interval uncertainty involves interval uncertainty with the goal of more assembled perception with reference to impreciseness. In this paper, a Riemann–Liouville fractional-order integral is constructed in Type 2 interval delineated vague encompassment. The exploration of fractional calculus is continued with the manifestation of Riemann–Liouville and Caputo fractional derivatives in the cited phenomenon. In addition, Type 2 interval Laplace transformation is proposed in this text. Conclusively, a mathematical model regarding economic lot maintenance is analyzed as a conceivable implementation of this theoretical advancement.

Keywords

• Riemann–Liouville fractional integration
• Riemann–Liouville fractional derivative
• Caputo fractional derivative
• Laplace transformation
• fractional calculus under uncertainty
• EPQ model