What question did this study set out to answer?

The aim is to analyze the well-posedness of nonlinear implicit fractional differential equations of complex order.

August 5, 2026MathematicsOpen Access

Well-Posedness of Nonlinear Implicit ψ-Hilfer Fractional Problems of Complex Order with Applications to an Oscillator with Saturating Feedback

View Full Paper

Ask AI

Bookmark

Authors

Randomized trial investigates well-posedness of nonlinear implicit equations in fractional systems, indicating their stability and applicability.

The aim is to analyze the well-posedness of nonlinear implicit fractional differential equations of complex order.
Transformed fractional Cauchy problem to a Volterra integral equation
Used fixed-point theory for existence and uniqueness
Developed Gronwall inequality for nonlocal memory effects
Established existence via Schaefer’s theorem and uniqueness via Banach’s theorem
Demonstrated four types of Ulam stability, ensuring small perturbations lead to small solution changes
Validated the theoretical framework on a fractional nonlinear oscillator with feedback

Sompong et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark

Randomized trial investigates well-posedness of nonlinear implicit equations in fractional systems, indicating their stability and applicability.