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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A New Approach to Computational Mathematics: Fractional Ratio Derivative ($FRD$)

Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 635--645 | DOI:10.5890/DNC.2025.12.002

Sambhu Raj P. R., Athira Vinay, Sasi Gopalan

Department of Mathematics, Cochin University of Science and Technology, Kerala, India

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Abstract

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 $(0<\alpha<1)$, and it is assumed to be differentiable in the same way that the Caputo derivative is. This article strengthened the theory of fractional ratio derivatives by explaining the fundamental features and providing an overview of the mean-value theorems and fractional partial derivatives. Also, The neural network model proposed here shows better accuracy while using $FRD$.

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