On the Perturbation–Iteration Algorithm for fractional differential equations

On the Perturbation–Iteration Algorithm for fractional differential equations

In this study, Perturbation–Iteration Algorithm, namely PIA, is applied to solve some types of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are compared with the results published in the literature by considering some FD...

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Main Authors: Mehmet Şenol, İ. Timuçin Dolapci
Format: Article
Language:English
Published: Elsevier 2016-01-01
Series:Journal of King Saud University: Science
Subjects:
Caputo fractional derivative
Fractional differential equations
Initial value problems
Perturbation–Iteration method
Online Access:http://www.sciencedirect.com/science/article/pii/S1018364715000816
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spelling doaj-c650bbaa651e4fcba5cc83fed2ced4152020-11-24T20:48:20ZengElsevierJournal of King Saud University: Science1018-36472016-01-01281697410.1016/j.jksus.2015.09.005On the Perturbation–Iteration Algorithm for fractional differential equationsMehmet Şenol0İ. Timuçin Dolapci1Department of Mathematics, Nevşehir Hacı Bektaş Veli University, 50300 Nevşehir, TurkeyDepartment of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, TurkeyIn this study, Perturbation–Iteration Algorithm, namely PIA, is applied to solve some types of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are compared with the results published in the literature by considering some FDEs. The results confirm that the PIA is a powerful, efficient and accurate method for solving nonlinear fractional differential equations.http://www.sciencedirect.com/science/article/pii/S1018364715000816Caputo fractional derivativeFractional differential equationsInitial value problemsPerturbation–Iteration method
collection DOAJ
language English
format Article
sources DOAJ
author Mehmet Şenol
İ. Timuçin Dolapci
spellingShingle Mehmet Şenol
İ. Timuçin Dolapci
On the Perturbation–Iteration Algorithm for fractional differential equations
Journal of King Saud University: Science
Caputo fractional derivative
Fractional differential equations
Initial value problems
Perturbation–Iteration method
author_facet Mehmet Şenol
İ. Timuçin Dolapci
author_sort Mehmet Şenol
title On the Perturbation–Iteration Algorithm for fractional differential equations
title_short On the Perturbation–Iteration Algorithm for fractional differential equations
title_full On the Perturbation–Iteration Algorithm for fractional differential equations
title_fullStr On the Perturbation–Iteration Algorithm for fractional differential equations
title_full_unstemmed On the Perturbation–Iteration Algorithm for fractional differential equations
title_sort on the perturbation–iteration algorithm for fractional differential equations
publisher Elsevier
series Journal of King Saud University: Science
issn 1018-3647
publishDate 2016-01-01
description In this study, Perturbation–Iteration Algorithm, namely PIA, is applied to solve some types of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are compared with the results published in the literature by considering some FDEs. The results confirm that the PIA is a powerful, efficient and accurate method for solving nonlinear fractional differential equations.
topic Caputo fractional derivative
Fractional differential equations
Initial value problems
Perturbation–Iteration method
url http://www.sciencedirect.com/science/article/pii/S1018364715000816
work_keys_str_mv AT mehmetsenol ontheperturbationiterationalgorithmforfractionaldifferentialequations
AT itimucindolapci ontheperturbationiterationalgorithmforfractionaldifferentialequations
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