Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems

The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary...

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Main Authors: Hammad Khalil, Mohammed Al-Smadi, Khaled Moaddy, Rahmat Ali Khan, Ishak Hashim
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/5601821
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author Hammad Khalil
Mohammed Al-Smadi
Khaled Moaddy
Rahmat Ali Khan
Ishak Hashim
author_facet Hammad Khalil
Mohammed Al-Smadi
Khaled Moaddy
Rahmat Ali Khan
Ishak Hashim
author_sort Hammad Khalil
collection DOAJ
description The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.
format Article
id doaj-art-e08fb9fad82c42318c660b6e061d5a6f
institution Kabale University
issn 1026-0226
1607-887X
language English
publishDate 2016-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-e08fb9fad82c42318c660b6e061d5a6f2025-02-03T06:07:08ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/56018215601821Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value ProblemsHammad Khalil0Mohammed Al-Smadi1Khaled Moaddy2Rahmat Ali Khan3Ishak Hashim4Department of Mathematics, The University of Poonch Rawalakot, Azad Jammu and Kashmir, PakistanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Mathematics, Faculty of Science and Arts, Shaqra University, Shaqra 11691, Saudi ArabiaDepartment of Mathematics, University of Malakand, Chakdara, Lower Dir, Khyber Pakhtunkhwa, PakistanSchool of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaThe paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.http://dx.doi.org/10.1155/2016/5601821
spellingShingle Hammad Khalil
Mohammed Al-Smadi
Khaled Moaddy
Rahmat Ali Khan
Ishak Hashim
Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
Discrete Dynamics in Nature and Society
title Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
title_full Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
title_fullStr Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
title_full_unstemmed Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
title_short Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
title_sort toward the approximate solution for fractional order nonlinear mixed derivative and nonlocal boundary value problems
url http://dx.doi.org/10.1155/2016/5601821
work_keys_str_mv AT hammadkhalil towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems
AT mohammedalsmadi towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems
AT khaledmoaddy towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems
AT rahmatalikhan towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems
AT ishakhashim towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems