A New Approach to Computational Mathematics: Fractional Ratio Derivative ($FRD$) - R., Sambhu Raj P.; Vinay, Athira; Gopalan, Sasi (Discontinuity, Nonlinearity, and Complexity, 2026)
This article introduces a new fractional operator named Fractional Ratio Derivative ($FRD$). The motivation for developing new fractional operators is usually driven by the constraints of traditional integer-order calculus, which inappropriately expresses complex systems and phenomena. $FRD$ can explain geometry, minimizing techniques, and features such as the chain rule, Leibniz rule, linearity, and semigroup structure. This allows us to see the geometry of the fractional derivative, which solves the problem with fractional derivatives caused by irregular geometry. $FRD$ is defined solely in the order $(0