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Jani, Haresh, Singh, Twinkle. (1404). Introducing the Jani Transform: A Novel Integral Approach for Modeling Differential Equations and Dynamical Systems in AI. پژوهشنامه مدیریت اجرایی, 15(1), 107-143. doi: 10.22080/cjms.2026.30834.1789
Haresh Jani; Twinkle Singh. "Introducing the Jani Transform: A Novel Integral Approach for Modeling Differential Equations and Dynamical Systems in AI". پژوهشنامه مدیریت اجرایی, 15, 1, 1404, 107-143. doi: 10.22080/cjms.2026.30834.1789
Jani, Haresh, Singh, Twinkle. (1404). 'Introducing the Jani Transform: A Novel Integral Approach for Modeling Differential Equations and Dynamical Systems in AI', پژوهشنامه مدیریت اجرایی, 15(1), pp. 107-143. doi: 10.22080/cjms.2026.30834.1789
Jani, Haresh, Singh, Twinkle. Introducing the Jani Transform: A Novel Integral Approach for Modeling Differential Equations and Dynamical Systems in AI. پژوهشنامه مدیریت اجرایی, 1404; 15(1): 107-143. doi: 10.22080/cjms.2026.30834.1789

Introducing the Jani Transform: A Novel Integral Approach for Modeling Differential Equations and Dynamical Systems in AI

Caspian Journal of Mathematical Sciences
دوره 15، شماره 1 - شماره پیاپی 29، 2026، صفحه 107-143    اصل مقاله (222.96 K)
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.30834.1789
نویسندگان
Haresh Jani* 1؛ Twinkle Singh2
1Shri Sad Vidya Mandal Institute of Technology
2Sardar Vallabhbhai National Institute of Technology
تاریخ دریافت: 27 آذر 1404،  تاریخ بازنگری: 27 بهمن 1404،  تاریخ پذیرش: 29 بهمن 1404 
چکیده
This work introduces the Jani Transform (JT), a novel integral transform with a gamma-distribution-inspired kernel, designed for solving complex differential equations and dynamical systems in Artificial Intelligence (AI) modeling. Unlike classical Laplace and Fourier transforms, JT is tailored for nonlinear, memory-dependent, and time-localized systems frequently encountered in Neural ODEs, reinforcement learning, spiking neural networks, and time-series forecasting. The paper develops the theoretical framework of JT, including its definition, properties, inverse formulation, and transform tables for common functions. Derivative properties are established to facilitate operational calculus. Several illustrative examples demonstrate how JT simplifies the solution of ODEs and PDEs in AI contexts, providing interpretable, closed-form solutions. Comparative analysis highlights JT’s adaptability to nonlinearities, probabilistic interpretability, and superior integration into AI workflows. Applications in signal decomposition, denoising, and feature extraction for machine learning pipelines are discussed, along with future research directions involving fractional dynamics, fuzzy systems, hybrid transforms, quantum AI, and energy-efficient modeling. The results position the Jani Transform as a mathematically elegant and practically powerful tool for advancing interpretable and efficient AI models.
کلیدواژه‌ها
Transform Methods in AI؛ Interpretability in AI Models؛ Nonlinear Dynamical Systems؛ Integral Transforms
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