Comparative Study of Fractional Heun’s Method and Fractional q-Heun’s Method for Solving Fractional Differential Equations

Obaida Aljabari; Shaher Momani; Iqbal M. Batiha; Mohammad Odeh

doi:10.18576/pfda/120103

Comparative Study of Fractional Heun’s Method and Fractional q-Heun’s Method for Solving Fractional Differential Equations

Obaida Aljabari
, Shaher Momani
, Iqbal M. Batiha
, Mohammad Odeh

Nonlinear Dynamic Research Centre (NDRC)

University of Jordan
Al-Zaytoonah University of Jordan
Philadelphia University

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

2 Scopus citations

Abstract

This paper aims to study the Fractional Heun’s Method (FHM) and the Fractional q-Heun’s Method (FqHM). It provides a detailed comparison of their numerical performance, accuracy, and error behavior when solving fractional initial value problems (FIVPs). Numerical simulations are presented to validate the theoretical results and highlight the advantages and limitations of both methods.

Original language	English
Pages (from-to)	37-56
Number of pages	20
Journal	Progress in Fractional Differentiation and Applications
Volume	12
Issue number	1
DOIs	https://doi.org/10.18576/pfda/120103
State	Published - 2026

Keywords

Fractional Calculus
Fractional Heun’s Method
Fractional q-Heun’s Method
Initial Value Problems
Numerical Analysis
q-Calculus

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abstract = "This paper aims to study the Fractional Heun{\textquoteright}s Method (FHM) and the Fractional q-Heun{\textquoteright}s Method (FqHM). It provides a detailed comparison of their numerical performance, accuracy, and error behavior when solving fractional initial value problems (FIVPs). Numerical simulations are presented to validate the theoretical results and highlight the advantages and limitations of both methods.",

keywords = "Fractional Calculus, Fractional Heun{\textquoteright}s Method, Fractional q-Heun{\textquoteright}s Method, Initial Value Problems, Numerical Analysis, q-Calculus",

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AU - Aljabari, Obaida

AU - Momani, Shaher

AU - Batiha, Iqbal M.

AU - Odeh, Mohammad

PY - 2026

Y1 - 2026

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AB - This paper aims to study the Fractional Heun’s Method (FHM) and the Fractional q-Heun’s Method (FqHM). It provides a detailed comparison of their numerical performance, accuracy, and error behavior when solving fractional initial value problems (FIVPs). Numerical simulations are presented to validate the theoretical results and highlight the advantages and limitations of both methods.

KW - Fractional Calculus

KW - Fractional Heun’s Method

KW - Fractional q-Heun’s Method

KW - Initial Value Problems

KW - Numerical Analysis

KW - q-Calculus

UR - https://www.scopus.com/pages/publications/105036107213

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DO - 10.18576/pfda/120103

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JO - Progress in Fractional Differentiation and Applications

JF - Progress in Fractional Differentiation and Applications

IS - 1

ER -

Comparative Study of Fractional Heun’s Method and Fractional q-Heun’s Method for Solving Fractional Differential Equations

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Keywords

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