Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions

Sabri T.M. Thabet; Imed Kedim; Mohammad Esmael Samei; Thabet Abdeljawad

doi:10.3846/mma.2025.22328

Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions

Sabri T.M. Thabet^*, Imed Kedim, Mohammad Esmael Samei, Thabet Abdeljawad^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

This manuscript investigates the qualitative analysis of a new hybrid fractional pantograph system involving Atangana-Baleanu-Caputo derivatives, complemented by hybrid integral boundary conditions. Dhage’s fixed point theorem is employed to investigate the existence theorem of the solutions, while uniqueness is proven by using Perov’s approach and Lipschitz’s matrix. The Hyers-Ulam (HU) stability is also demonstrated using the Lip-schitz’s matrix and techniques from nonlinear analysis. Finally, illustrative example is enhanced to examine the effectiveness of the obtained results.

Original language	English
Pages (from-to)	386-404
Number of pages	19
Journal	Mathematical Modelling and Analysis
Volume	30
Issue number	2
DOIs	https://doi.org/10.3846/mma.2025.22328
Publication status	Published - 18 Apr 2025
Externally published	Yes

Keywords

Caputo-Atangana-Baleanu operator
Dhage and Perov techniques
Lipschitzian’s matrix
coupled hybrid fractional differential system
pantograph problem

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title = "Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions",

abstract = "This manuscript investigates the qualitative analysis of a new hybrid fractional pantograph system involving Atangana-Baleanu-Caputo derivatives, complemented by hybrid integral boundary conditions. Dhage{\textquoteright}s fixed point theorem is employed to investigate the existence theorem of the solutions, while uniqueness is proven by using Perov{\textquoteright}s approach and Lipschitz{\textquoteright}s matrix. The Hyers-Ulam (HU) stability is also demonstrated using the Lip-schitz{\textquoteright}s matrix and techniques from nonlinear analysis. Finally, illustrative example is enhanced to examine the effectiveness of the obtained results.",

keywords = "Caputo-Atangana-Baleanu operator, Dhage and Perov techniques, Lipschitzian{\textquoteright}s matrix, coupled hybrid fractional differential system, pantograph problem",

author = "Thabet, \{Sabri T.M.\} and Imed Kedim and Samei, \{Mohammad Esmael\} and Thabet Abdeljawad",

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doi = "10.3846/mma.2025.22328",

language = "English",

volume = "30",

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journal = "Mathematical Modelling and Analysis",

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AU - Thabet, Sabri T.M.

AU - Kedim, Imed

AU - Samei, Mohammad Esmael

AU - Abdeljawad, Thabet

PY - 2025/4/18

Y1 - 2025/4/18

N2 - This manuscript investigates the qualitative analysis of a new hybrid fractional pantograph system involving Atangana-Baleanu-Caputo derivatives, complemented by hybrid integral boundary conditions. Dhage’s fixed point theorem is employed to investigate the existence theorem of the solutions, while uniqueness is proven by using Perov’s approach and Lipschitz’s matrix. The Hyers-Ulam (HU) stability is also demonstrated using the Lip-schitz’s matrix and techniques from nonlinear analysis. Finally, illustrative example is enhanced to examine the effectiveness of the obtained results.

AB - This manuscript investigates the qualitative analysis of a new hybrid fractional pantograph system involving Atangana-Baleanu-Caputo derivatives, complemented by hybrid integral boundary conditions. Dhage’s fixed point theorem is employed to investigate the existence theorem of the solutions, while uniqueness is proven by using Perov’s approach and Lipschitz’s matrix. The Hyers-Ulam (HU) stability is also demonstrated using the Lip-schitz’s matrix and techniques from nonlinear analysis. Finally, illustrative example is enhanced to examine the effectiveness of the obtained results.

KW - Caputo-Atangana-Baleanu operator

KW - Dhage and Perov techniques

KW - Lipschitzian’s matrix

KW - coupled hybrid fractional differential system

KW - pantograph problem

UR - https://www.scopus.com/pages/publications/105007227826

U2 - 10.3846/mma.2025.22328

DO - 10.3846/mma.2025.22328

M3 - Article

AN - SCOPUS:105007227826

SN - 1392-6292

VL - 30

SP - 386

EP - 404

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

IS - 2

ER -

Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions

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Keywords

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