Marisa Kaewsuwan, Chatthai Thaiprayoon, Aphirak Aphithana, Jutarat Kongson, Weerapan Sae-dan, Weerawat Sudsutad, Nonlinear impulsive $(\rho_k,\psi_k)$-Hilfer fractional pantograph integro-differential equations under nonlocal integral boundary conditions, Vol. 2024 (2024), Article ID 10, pp. 1-29

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DOI: 10.23952/jnfa.2024.10

Received October 21, 2023; Accepted March 10, 2024; Published May 6, 2024

Abstract. This paper investigates the existence and uniqueness of solutions for a class of nonlinear impulsive fractional pantograph integro–differential equations with multi-point integral boundary conditions in the context of the $(\rho_{k},\psi_{k})$ -Hilfer fractional operator. We transform our problem into an equivalent integral equation, and the uniqueness result is proved by applying Banach’s fixed-point theorem. In addition, some types of Ulam’s stability results are demonstrated and numerical examples are designed to illustrate the applicability of our theoretical results.

How to Cite this Article:
M. Kaewsuwan, C. Thaiprayoon, A. Aphithana, J. Kongson, W. Sae-dan, W. Sudsutad, Nonlinear impulsive $(\rho_k,\psi_k)$ -Hilfer fractional pantograph integro-differential equations under nonlocal integral boundary conditions, J. Nonlinear Funct. Anal. 2024 (2024) 10.