UPPER AND LOWER SOLUTION METHODS FOR IMPULSIVE CAPUTO–HADAMARD FRACTIONAL DIFFERENTIAL INCLUSIONS

Amouria Hammou; Samira Hamani; Johnny Henderson

doi:10.1216/rmj.2023.53.1817

Abstract

We investigate the existence of solutions for a class of initial value problems for impulsive Caputo–Hadamard fractional differential inclusions of order $r\in(1,2\rbrack$ . We apply the concept of lower and upper solutions combined with the Bohnenblust–Karlin fixed point theorem.

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Amouria Hammou. Samira Hamani. Johnny Henderson. "UPPER AND LOWER SOLUTION METHODS FOR IMPULSIVE CAPUTO–HADAMARD FRACTIONAL DIFFERENTIAL INCLUSIONS." Rocky Mountain J. Math. 53 (6) 1817 - 1831, December 2023. https://doi.org/10.1216/rmj.2023.53.1817

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Received: 8 March 2022; Revised: 5 June 2022; Accepted: 5 June 2022; Published: December 2023

First available in Project Euclid: 21 December 2023

MathSciNet: MR4682744

zbMATH: 07784576

Digital Object Identifier: 10.1216/rmj.2023.53.1817

Subjects:

Primary: 26A33

Keywords: Caputo–Hadamard fractional derivative , fixed point Theorem , fractional differential inclusion , fractional integral , Impulsive , Initial value problem

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