Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 65, pp. 1-20.

Title: Three-point integral boundary-value problems for piecewise fractional impulsive
differential equations with p-Laplacian operator

Authors: Xiao Chen (Lanzhou Jiaotong Univ., Gansu, China)
         Wenxue Zhou (Lanzhou Jiaotong Univ., Gansu, China)

Abstract:
We study the existence and uniqueness of solutions for three-point integral
boundary-value problems of piecewise fractional impulsive differential 
equations with $p$-Laplacian operator and delay.
We prove the existence of solutions, by using the $\psi$-Hadamard fractional 
definition, the Leray-Schauder nonlinear alternative, and the Krasnosel'skiis fixed 
point theorem. 
Subsequently, we prove uniqueness of the solution using the Banach fixed point theorem. 
To verify the feasibility of the main results, we give two examples.

Submitted February 24, 2025. Published June 30, 2025.
Math Subject Classifications: 34B15, 34B30, 34B37, 45J05.
Key Words: psi-Hadamard fractional derivative; p-Laplacian operator; impulsive; delay.