α-Conformable Fractional Lebesgue Type Measure and Sub-measure (European Journal of Pure and Applied Mathematics, 2026)
In this paper, based on the α-conformable fractional derivative and integral, we give definitions for both Lebesgue measure and submeasure in the fractional sense. The α-conformable fractional Lebesguetype measures and sub-measures provide powerful generalizations of classical Lebesgue measure and sub-measure, enabling the analysis of non-standard complex spaces and phenomena. Their applications extend beyond pure mathematics to fields such as quantum physics, modeling fractional market dynamics, fractional probability theory, and pattern recognition for AI and machine learning.
Keywords: α-conformable fractional measure; α-conformable fractional sub-measure; α-conformable fractional Lesbegue space