Scipediacontent: Scipediacontent moved page Review 994593194266 to Alhwikem Awadalla 2026a

2026-05-08T07:57:49Z

Scipediacontent moved page Review 994593194266 to Alhwikem Awadalla 2026a

Scipediacontent: Scipediacontent moved page Draft content 562676460 to Review 994593194266

2026-05-08T07:55:32Z

Scipediacontent moved page Draft content 562676460 to Review 994593194266

Scipediacontent: Created page with " == Abstract ==
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving gen..."

2026-05-08T07:55:24Z

Created page with " == Abstract == This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving gen..."

New page

== Abstract ==

This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving generalized Caputo derivatives. The system’s hybrid nature, coupled with the generality of the fractional operators, allows for modeling complex interdependent processes with memory effects that cannot be adequately captured by existing models. 
Using Krasnoselskii’s fixed point theorem, we prove the existence of at least one solution under explicit coupling conditions. Under appropriate Lipschitz conditions, we establish uniqueness via Banach’s contraction principle, deriving a quantitative condition involving the fractional orders, generalization parameters, and Lipschitz constants. We also conduct a rigorous analysis of Ulam-Hyers and Ulam-Hyers-Rassias stability, obtaining explicit stability constants that provide quantitative bounds on how perturbations in the input affect the solution. 
The theoretical results are validated through three carefully constructed numerical examples with explicit parameter values demonstrating existence, uniqueness, and Ulam-Hyers stability. A parameter sensitivity analysis confirms the robustness of the uniqueness condition across variations in fractional orders, generalization parameters, and interval lengths. The paper concludes with a discussion of limitations and directions for future research, including extensions to higher fractional orders, delay and impulsive effects, and numerical methods.

== Document ==
<pdf>Media:Draft_content_562676460-3683-document.pdf</pdf>

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Alhwikem Awadalla 2026a - Revision history

Scipediacontent: Scipediacontent moved page Review 994593194266 to Alhwikem Awadalla 2026a

Scipediacontent: Scipediacontent moved page Draft content 562676460 to Review 994593194266

Scipediacontent: Created page with " == Abstract == This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving gen..."

Scipediacontent: Created page with " == Abstract ==
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving gen..."