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Impulsive nonlocal boundary value problems for ( k , ψ )-Hilfer proportional fractional differential equations: Existence, stability, and application to pantograph equations
AIMS Mathematics 2026, 11(5): 14558-14585
Published: 15 May 2026
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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.

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