On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals

Abstract In this research paper, we introduce a general structure of a fractional boundary value problem in which a 2-term fractional differential equation has a fractional bi-order setting of Riemann–Liouville type. Moreover, we consider the boundary conditions of the proposed problem as mixed Riem...

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Main Authors:	Salim Ben Chikh, Abdelkader Amara, Sina Etemad, Shahram Rezapour
Format:	Article
Language:	English
Published:	SpringerOpen 2020-10-01
Series:	Advances in Difference Equations
Subjects:	Boundary value problem Hyers–Ulam stability Multi-order fractional differential equation Riemann–Liouville derivative
Online Access:	http://link.springer.com/article/10.1186/s13662-020-03012-1

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spelling	doaj-d8979c9379c54a038fc2592af8b50a0b2020-11-25T01:59:33ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020112010.1186/s13662-020-03012-1On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integralsSalim Ben Chikh0Abdelkader Amara1Sina Etemad2Shahram Rezapour3Laboratory of Applied Mathematics, University of Kasdi MerbahLaboratory of Applied Mathematics, University of Kasdi MerbahDepartment of Mathematics, Azarbaijan Shahid Madani UniversityInstitute of Research and Development, Duy Tan UniversityAbstract In this research paper, we introduce a general structure of a fractional boundary value problem in which a 2-term fractional differential equation has a fractional bi-order setting of Riemann–Liouville type. Moreover, we consider the boundary conditions of the proposed problem as mixed Riemann–Liouville integro-derivative conditions with four different orders which cover many special cases studied before. In the first step, we investigate the existence and uniqueness of solutions for the given multi-order boundary value problem, and then the Hyers–Ulam stability is another notion in this regard which we study. Finally, we provide two illustrative examples to support our theoretical findings.http://link.springer.com/article/10.1186/s13662-020-03012-1Boundary value problemHyers–Ulam stabilityMulti-order fractional differential equationRiemann–Liouville derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Salim Ben Chikh Abdelkader Amara Sina Etemad Shahram Rezapour
spellingShingle	Salim Ben Chikh Abdelkader Amara Sina Etemad Shahram Rezapour On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals Advances in Difference Equations Boundary value problem Hyers–Ulam stability Multi-order fractional differential equation Riemann–Liouville derivative
author_facet	Salim Ben Chikh Abdelkader Amara Sina Etemad Shahram Rezapour
author_sort	Salim Ben Chikh
title	On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals
title_short	On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals
title_full	On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals
title_fullStr	On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals
title_full_unstemmed	On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals
title_sort	on hyers–ulam stability of a multi-order boundary value problems via riemann–liouville derivatives and integrals
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-10-01
description	Abstract In this research paper, we introduce a general structure of a fractional boundary value problem in which a 2-term fractional differential equation has a fractional bi-order setting of Riemann–Liouville type. Moreover, we consider the boundary conditions of the proposed problem as mixed Riemann–Liouville integro-derivative conditions with four different orders which cover many special cases studied before. In the first step, we investigate the existence and uniqueness of solutions for the given multi-order boundary value problem, and then the Hyers–Ulam stability is another notion in this regard which we study. Finally, we provide two illustrative examples to support our theoretical findings.
topic	Boundary value problem Hyers–Ulam stability Multi-order fractional differential equation Riemann–Liouville derivative
url	http://link.springer.com/article/10.1186/s13662-020-03012-1
work_keys_str_mv	AT salimbenchikh onhyersulamstabilityofamultiorderboundaryvalueproblemsviariemannliouvillederivativesandintegrals AT abdelkaderamara onhyersulamstabilityofamultiorderboundaryvalueproblemsviariemannliouvillederivativesandintegrals AT sinaetemad onhyersulamstabilityofamultiorderboundaryvalueproblemsviariemannliouvillederivativesandintegrals AT shahramrezapour onhyersulamstabilityofamultiorderboundaryvalueproblemsviariemannliouvillederivativesandintegrals
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On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals

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