A New Fractional Representation of the Higher Order Taylor Scheme

Iqbal M. Batiha; Iqbal H. Jebril; Amira Abdelnebi; Zoubir Dahmani; Shawkat Alkhazaleh; Nidal Anakira

doi:10.1155/2024/2849717

A New Fractional Representation of the Higher Order Taylor Scheme

Iqbal M. Batiha
, Iqbal H. Jebril
, Amira Abdelnebi
, Zoubir Dahmani
, Shawkat Alkhazaleh
, Nidal Anakira

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Mostaganem
University of Blida 1
Jadara University
Sohar University

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

10 Scopus citations

Abstract

In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

Original language	English
Article number	2849717
Journal	Computational and Mathematical Methods
Volume	2024
DOIs	https://doi.org/10.1155/2024/2849717
State	Published - 2024

Keywords

Caputo fractional derivative operator
generalized Taylor’s theorem
higher order Taylor method
local truncation error

Access to Document

10.1155/2024/2849717

Cite this

@article{8e5ee1ea5516445db637a94de456f3c9,

title = "A New Fractional Representation of the Higher Order Taylor Scheme",

abstract = "In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.",

keywords = "Caputo fractional derivative operator, generalized Taylor{\textquoteright}s theorem, higher order Taylor method, local truncation error",

author = "Batiha, \{Iqbal M.\} and Jebril, \{Iqbal H.\} and Amira Abdelnebi and Zoubir Dahmani and Shawkat Alkhazaleh and Nidal Anakira",

note = "Publisher Copyright: {\textcopyright} 2024 Iqbal M. Batiha et al.",

year = "2024",

doi = "10.1155/2024/2849717",

language = "English",

volume = "2024",

journal = "Computational and Mathematical Methods",

issn = "2577-7408",

publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - A New Fractional Representation of the Higher Order Taylor Scheme

AU - Batiha, Iqbal M.

AU - Jebril, Iqbal H.

AU - Abdelnebi, Amira

AU - Dahmani, Zoubir

AU - Alkhazaleh, Shawkat

AU - Anakira, Nidal

PY - 2024

Y1 - 2024

N2 - In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

AB - In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

KW - Caputo fractional derivative operator

KW - generalized Taylor’s theorem

KW - higher order Taylor method

KW - local truncation error

UR - https://www.scopus.com/pages/publications/85192907099

U2 - 10.1155/2024/2849717

DO - 10.1155/2024/2849717

M3 - Article

AN - SCOPUS:85192907099

SN - 2577-7408

VL - 2024

JO - Computational and Mathematical Methods

JF - Computational and Mathematical Methods

M1 - 2849717

ER -

A New Fractional Representation of the Higher Order Taylor Scheme

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this