Applicability of Caputo-Hadmard fractional operator in mathematical modeling of pantograph systems

Muath Awadallah; Mohamed Hannabou; Hajer Zaway; Jihan Alahmadi

doi:10.1007/s12190-025-02421-3

Applicability of Caputo-Hadmard fractional operator in mathematical modeling of pantograph systems

Muath Awadallah
, Mohamed Hannabou
, Hajer Zaway
, Jihan Alahmadi

Mathematics

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

2 Scopus citations

Abstract

This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer’s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.

Original language	English
Pages (from-to)	4971-4986
Number of pages	16
Journal	Journal of Applied Mathematics and Computing
Volume	71
Issue number	4
DOIs	https://doi.org/10.1007/s12190-025-02421-3
State	Published - Aug 2025

Keywords

Caputo-Hadamard fractional derivative
Existence and uniqueness
Fixed point theorems
Pantograph fractional differential equations

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10.1007/s12190-025-02421-3

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title = "Applicability of Caputo-Hadmard fractional operator in mathematical modeling of pantograph systems",

abstract = "This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer{\textquoteright}s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.",

keywords = "Caputo-Hadamard fractional derivative, Existence and uniqueness, Fixed point theorems, Pantograph fractional differential equations",

author = "Muath Awadallah and Mohamed Hannabou and Hajer Zaway and Jihan Alahmadi",

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AU - Awadallah, Muath

AU - Hannabou, Mohamed

AU - Zaway, Hajer

AU - Alahmadi, Jihan

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.

PY - 2025/8

Y1 - 2025/8

N2 - This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer’s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.

AB - This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer’s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.

KW - Caputo-Hadamard fractional derivative

KW - Existence and uniqueness

KW - Fixed point theorems

KW - Pantograph fractional differential equations

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JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 4

ER -

Applicability of Caputo-Hadmard fractional operator in mathematical modeling of pantograph systems

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