Scipediacontent: Scipediacontent moved page Review 910108924005 to Tandogdu et al 2026a

2026-01-07T10:25:36Z

Scipediacontent moved page Review 910108924005 to Tandogdu et al 2026a

JSanchez: JSanchez moved page Draft Sanchez Pinedo 637245973 to Review 910108924005

2026-01-07T10:18:27Z

JSanchez moved page Draft Sanchez Pinedo 637245973 to Review 910108924005

JSanchez: Created page with " == Abstract ==
Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non i..."

2026-01-07T10:18:25Z

Created page with " == Abstract == <p>Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non i..."

New page

== Abstract ==

<p>Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non integer order calculus is considered is a field where a vast spectrum of studies can be undertaken. The purpose of this study introduces a novel fractional-order quadratic regression model grounded in the Caputo derivative framework, addressing the limitation and the rigidity of classical polynomial regression in adapting to the intrinsic curvature of data. The core innovation is the use of the fractional order ν as a tunable parameter for curvature-sensitive optimization. Our main contributions are fourfold: First, we establish a fundamental theoretical pillar by proving that the second-order Caputo derivative preserves the curvature direction of quadratic functions, enabling a principled optimization framework. Second, we rigorously demonstrate the model’s robustness by proving the existence and uniqueness of solutions via Banach’s fixed point theorem and establishing stability bounds through a fractional Grönwall inequality. Third, we develop a practical methodology to identify an optimal fractional order ν that minimizes the error-to-explained-variation ratio (SSE/SSR). Finally, we validate the framework on four diverse real-world datasets from air quality, soil science, education, and meteorology. The proposed model consistently outperforms classical quadratic regression, achieving a reduction in the SSE/SSR ratio by up to 21% in specific cases. The proposed method yields more efficient models with either lower estimation error or higher correlation coefficients, positioning Caputo fractional quadratic regression as a powerful and theoretically sound alternative for modeling cases where quadratic regression is considered appropriate.OPEN ACCESS Received: 10/09/2025 Accepted: 05/11/2025</p>

== Document ==
<pdf>Media:Draft_Sanchez Pinedo_637245973-3209-document.pdf</pdf>

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Tandogdu et al 2026a - Revision history

Scipediacontent: Scipediacontent moved page Review 910108924005 to Tandogdu et al 2026a

JSanchez: JSanchez moved page Draft Sanchez Pinedo 637245973 to Review 910108924005

JSanchez: Created page with " == Abstract == Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non i..."

JSanchez: Created page with " == Abstract ==
Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non i..."