6 papers
A Semigroup Approach to Weighted Weyl-Sonine Operators: Bypassing Bernstein Functions for Well-Posedness
Gustavo Dorrego
This paper establishes a rigorous functional analytic framework for weighted Weyl-Sonine fractional operators on semi-infinite intervals. While the classical Phillips functional ca…
A Fractional Fox H-Function Kernel for Support Vector Machines: Robust Classification via Weighted Transmutation Operators
Gustavo Dorrego
Support Vector Machines (SVMs) rely heavily on the choice of the kernel function to map data into high-dimensional feature spaces. While the Gaussian Radial Basis Function (RBF) is…
Beyond the Markovian Assumption: Robust Optimization via Fractional Weyl Integrals in Imbalanced Data
Gustavo A. Dorrego
Standard Gradient Descent and its modern variants assume local, Markovian weight updates, making them highly susceptible to noise and overfitting. This limitation becomes criticall…
Weighted Sobolev Spaces and Distributional Spectral Theory for Generalized Aging Operators via Transmutation Methods
Gustavo Dorrego
The spectral analysis of operators in heterogeneous and aging media typically requires a functional framework that extends beyond the standard Hilbertian setting. In this paper, we…
A Unified Spectral Framework for Aging, Heterogeneous, and Distributed Order Systems via Weighted Weyl-Sonine Operators
Gustavo Dorrego
While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line…
Spectral Analysis of Weighted Weyl Fractional Operators: Aging, Infinite Memory, and the Amnesia Effect
Gustavo Dorrego
This paper establishes a rigorous spectral framework for the Weighted Weyl Fractional Calculus, designed to model non-local systems exhibiting aging and subjective time scales. By…