Fractional Ibaguner-IFO Operators and Infrared Phase Transition in Sobolev-Type Inequalities

Key Points

• The aim is to derive new Sobolev-type inequalities using fractional IFO operators and investigate the phase transition behavior as parameters vary.
• Derived a new Sobolev-type inequality with fractional IFO operators.
• Applied exponential infrared regularization.
• Conducted numerical simulations to support theoretical findings.
• Established a rigorous phase transition as the parameter approaches zero.
• Numerical simulations confirmed the theoretical results, demonstrating infrared control's importance.