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The study aims to explore impulsive tempered Ψ-fractional differential equations and their implications in dynamic systems.

February 8, 2026Fractal and FractionalOpen Access

Impulsive Tempered Ψ-Fractional Differential Equations with Boundary and Integral Conditions

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Demonstrates solutions for mixed impulsive boundary value problems, suggesting enhanced modeling capabilities.

The study aims to explore impulsive tempered Ψ-fractional differential equations and their implications in dynamic systems.
Introduced exponential tempering in Ψ-fractional derivatives
Reformulated problems as Volterra integral equations
Applied fixed-point theory for analytical results
Proved existence and uniqueness using Banach Contraction Mapping Principle
Ensured existence through Leray–Schauder nonlinear alternative
Showed existence and uniqueness of solutions for the proposed equations
Demonstrated effectiveness of tempered fractional framework for modeling
Illustrated the applicability of methods with a numerical example
Found improvements over conventional power-law kernels for systems with fading memory

Sudprasert et al. (2026) studied this question.

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