@article{Sudsutad2026, 
author = {Weerawat Sudsutad and Chatthai Thaiprayoon and Jutarat Kongson and Aphirak Aphithana},
title = {Impulsive nonlocal boundary value problems for    (  k  ,  ψ  )-Hilfer proportional fractional differential equations: Existence, stability, and application to pantograph equations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14558-14585},
keywords = {(k, ψ)-Hilfer proportional fractional operator, impulsive conditions, nonlocal integral boundary conditions, existence and uniqueness, Ulam-Hyers stability},
url = {https://www.sciopen.com/article/10.3934/math.2026597},
doi = {10.3934/math.2026597},
abstract = {This paper examines a class of impulsive boundary value problems related to fractional pantograph differential equations governed by the    (  k  ,  ψ  )-Hilfer proportional fractional derivative. The problem is reformulated into an equivalent integral equation, which provides a convenient framework for further analysis. The existence and uniqueness of solutions are derived using Banach's fixed-point theorem. Moreover, several forms of Ulam stability are examined. Illustrative examples and graphical computations are included to support the applicability of the theoretical results.}
}