On the Duality of the Natural Transform with Anuj, Rishi, Elzaki, Sawi, Mohand, Kamal, ARA Transforms

Authors : Hatice Muti, Gaye Yeşim Taflan

Pages : 783-794

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Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :In this study, the duality between the Natural transform and the Anuj, Sawi, Elzaki, Kamal, Rishi, Mohand, ARA, and Shehu transforms is systematically investigated. We chose these transforms because they are widely used in the literature. These transforms, many of which are recent developments in operational calculus, are examined in the context of their structural similarities and their behavior when applied to a representative function. To illustrate this duality, we compute and graphically compare the transforms of a chosen function under each method. The analysis highlights not only the computational and theoretical affinities between the transforms but also their respective efficiencies and distinctive features. This comparative approach provides new insights into the interconnected nature of integral transforms and their applicability in solving differential and integral equations across various domains of applied mathematics.
Keywords : Integral dönüşüm, Naturel dönüşümün dualitesi, Elzaki dönüşümü, Rishi dönüşümü, ARA dönüşümü, Sawi dönüşümü

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