A NEW FRACTIONAL APPROACH FOR THE HIGHER-ORDER q-TAYLOR METHOD

Nadia Allouch; Iqbal M. Batiha; Iqbal H. Jebril; Samira Hamani; Areen Al-Khateeb; Shaher Momani

doi:10.5566/IAS.3286

A NEW FRACTIONAL APPROACH FOR THE HIGHER-ORDER q-TAYLOR METHOD

Nadia Allouch
, Iqbal M. Batiha
, Iqbal H. Jebril
, Samira Hamani
, Areen Al-Khateeb
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

University of Mostaganem
Al-Zaytoonah University of Jordan
Jadara University
University of Jordan

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

10 Scopus citations

Abstract

The main goal of this work is to propose a new fractional approach of the higher-order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM’s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximate solution obtained by (FHOqTM).

Original language	English
Pages (from-to)	249-257
Number of pages	9
Journal	Image Analysis and Stereology
Volume	43
Issue number	3
DOIs	https://doi.org/10.5566/IAS.3286
State	Published - 2024

Keywords

Caputo q-derivative
Fractional q-difference equations
Generalized q-Taylor theorem
Higher-order q-Taylor method

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10.5566/IAS.3286

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@article{6e870fc238b748ad8c4cce0bc1c6656b,

title = "A NEW FRACTIONAL APPROACH FOR THE HIGHER-ORDER q-TAYLOR METHOD",

abstract = "The main goal of this work is to propose a new fractional approach of the higher-order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM{\textquoteright}s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximate solution obtained by (FHOqTM).",

keywords = "Caputo q-derivative, Fractional q-difference equations, Generalized q-Taylor theorem, Higher-order q-Taylor method",

author = "Nadia Allouch and Batiha, \{Iqbal M.\} and Jebril, \{Iqbal H.\} and Samira Hamani and Areen Al-Khateeb and Shaher Momani",

year = "2024",

doi = "10.5566/IAS.3286",

language = "English",

volume = "43",

pages = "249--257",

journal = "Image Analysis and Stereology",

issn = "1580-3139",

publisher = "Slovenian Society For Stereology And Quantitative Image Analysis",

number = "3",

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TY - JOUR

T1 - A NEW FRACTIONAL APPROACH FOR THE HIGHER-ORDER q-TAYLOR METHOD

AU - Allouch, Nadia

AU - Batiha, Iqbal M.

AU - Jebril, Iqbal H.

AU - Hamani, Samira

AU - Al-Khateeb, Areen

AU - Momani, Shaher

PY - 2024

Y1 - 2024

N2 - The main goal of this work is to propose a new fractional approach of the higher-order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM’s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximate solution obtained by (FHOqTM).

AB - The main goal of this work is to propose a new fractional approach of the higher-order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM’s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximate solution obtained by (FHOqTM).

KW - Caputo q-derivative

KW - Fractional q-difference equations

KW - Generalized q-Taylor theorem

KW - Higher-order q-Taylor method

UR - https://www.scopus.com/pages/publications/85211507706

U2 - 10.5566/IAS.3286

DO - 10.5566/IAS.3286

M3 - Article

AN - SCOPUS:85211507706

SN - 1580-3139

VL - 43

SP - 249

EP - 257

JO - Image Analysis and Stereology

JF - Image Analysis and Stereology

IS - 3

ER -

A NEW FRACTIONAL APPROACH FOR THE HIGHER-ORDER q-TAYLOR METHOD

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Keywords

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