This paper examines a class of impulsive boundary value problems related to fractional pantograph differential equations governed by the $ (k, \psi) $-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.
Citation: Weerawat Sudsutad, Chatthai Thaiprayoon, Jutarat Kongson, Aphirak Aphithana. Impulsive nonlocal boundary value problems for $ (k, \psi) $-Hilfer proportional fractional differential equations: Existence, stability, and application to pantograph equations[J]. AIMS Mathematics, 2026, 11(5): 14558-14585. doi: 10.3934/math.2026597
This paper examines a class of impulsive boundary value problems related to fractional pantograph differential equations governed by the $ (k, \psi) $-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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Weerawat Sudsutad, Chatthai Thaiprayoon, Jutarat Kongson, Aphirak Aphithana. Impulsive nonlocal boundary value problems for $ (k, \psi) $-Hilfer proportional fractional differential equations: Existence, stability, and application to pantograph equations[J]. AIMS Mathematics, 2026, 11(5): 14558-14585. doi: 10.3934/math.2026597
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