Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations

Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations

We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii’s and Banach’...

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Main Authors: Zareen A. Khan, Israr Ahmad, Kamal Shah
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2021/1399764
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spelling doaj-dc986ccab7fb4c5f9bb064459e4de90a2021-10-11T00:38:46ZengHindawi LimitedJournal of Function Spaces2314-88882021-01-01202110.1155/2021/1399764Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential EquationsZareen A. Khan0Israr Ahmad1Kamal Shah2College of ScienceDepartment of MathematicsDepartment of MathematicsWe investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii’s and Banach’s fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided.http://dx.doi.org/10.1155/2021/1399764
collection DOAJ
language English
format Article
sources DOAJ
author Zareen A. Khan
Israr Ahmad
Kamal Shah
spellingShingle Zareen A. Khan
Israr Ahmad
Kamal Shah
Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
Journal of Function Spaces
author_facet Zareen A. Khan
Israr Ahmad
Kamal Shah
author_sort Zareen A. Khan
title Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
title_short Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
title_full Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
title_fullStr Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
title_full_unstemmed Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
title_sort applications of fixed point theory to investigate a system of fractional order differential equations
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8888
publishDate 2021-01-01
description We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii’s and Banach’s fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided.
url http://dx.doi.org/10.1155/2021/1399764
work_keys_str_mv AT zareenakhan applicationsoffixedpointtheorytoinvestigateasystemoffractionalorderdifferentialequations
AT israrahmad applicationsoffixedpointtheorytoinvestigateasystemoffractionalorderdifferentialequations
AT kamalshah applicationsoffixedpointtheorytoinvestigateasystemoffractionalorderdifferentialequations
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