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Solving fractional differential equations using fractional explicit method

This research is focusing in solving the fractional differential equations (FDEs) for linear and non-linear type using fractional explicit method (FEM) with constant step-size. Most of the numerical methods for solving FDEs involved the interpolating points of step size ℎ. Some modifications were im...

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Main Authors: Yiung, Yip Lian, Abdul Majid, Zanariah
Format: Article
Published: Universiti Kebangsaan Malaysia 2024
Online Access:http://psasir.upm.edu.my/id/eprint/108777/
https://www.ukm.my/jqma/jqma20-1/
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spelling my.upm.eprints.1087772024-09-26T07:29:04Z http://psasir.upm.edu.my/id/eprint/108777/ Solving fractional differential equations using fractional explicit method Yiung, Yip Lian Abdul Majid, Zanariah This research is focusing in solving the fractional differential equations (FDEs) for linear and non-linear type using fractional explicit method (FEM) with constant step-size. Most of the numerical methods for solving FDEs involved the interpolating points of step size ℎ. Some modifications were implemented in the derivation technique, where the step size 2ℎ are considered in the formula of the proposed method. The main goal of this research is to derive FEM by considering the implementation of second-order Adam-Bashforth method using Lagrange interpolation for fractional case. Besides, the order and convergence analysis of the developed method will also be investigated in this study. The algorithm of the proposed method is written in C language. Based on the numerical results obtained, it is clearly ratified that the proposed method converges as the step size, ℎ is getting smaller in solving the FDEs. Universiti Kebangsaan Malaysia 2024 Article PeerReviewed Yiung, Yip Lian and Abdul Majid, Zanariah (2024) Solving fractional differential equations using fractional explicit method. Journal of Quality Measurement and Analysis, 20 (1). pp. 41-55. ISSN 1823-5670; ESSN: 2600-8602 https://www.ukm.my/jqma/jqma20-1/ 10.17576/jqma.2001.2024.04
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description This research is focusing in solving the fractional differential equations (FDEs) for linear and non-linear type using fractional explicit method (FEM) with constant step-size. Most of the numerical methods for solving FDEs involved the interpolating points of step size ℎ. Some modifications were implemented in the derivation technique, where the step size 2ℎ are considered in the formula of the proposed method. The main goal of this research is to derive FEM by considering the implementation of second-order Adam-Bashforth method using Lagrange interpolation for fractional case. Besides, the order and convergence analysis of the developed method will also be investigated in this study. The algorithm of the proposed method is written in C language. Based on the numerical results obtained, it is clearly ratified that the proposed method converges as the step size, ℎ is getting smaller in solving the FDEs.
format Article
author Yiung, Yip Lian
Abdul Majid, Zanariah
spellingShingle Yiung, Yip Lian
Abdul Majid, Zanariah
Solving fractional differential equations using fractional explicit method
author_facet Yiung, Yip Lian
Abdul Majid, Zanariah
author_sort Yiung, Yip Lian
title Solving fractional differential equations using fractional explicit method
title_short Solving fractional differential equations using fractional explicit method
title_full Solving fractional differential equations using fractional explicit method
title_fullStr Solving fractional differential equations using fractional explicit method
title_full_unstemmed Solving fractional differential equations using fractional explicit method
title_sort solving fractional differential equations using fractional explicit method
publisher Universiti Kebangsaan Malaysia
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/108777/
https://www.ukm.my/jqma/jqma20-1/
_version_ 1811686026771431424
score 13.244368

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