Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed...

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Main Authors: Lizhen Chen, Gang Li
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/2761321
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spelling doaj-6159dc3cbc7346a1bca54c616d913d3d2020-11-25T00:23:55ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/27613212761321Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial ConditionsLizhen Chen0Gang Li1School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, ChinaSchool of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, ChinaIn this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.http://dx.doi.org/10.1155/2018/2761321
collection DOAJ
language English
format Article
sources DOAJ
author Lizhen Chen
Gang Li
spellingShingle Lizhen Chen
Gang Li
Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
Journal of Function Spaces
author_facet Lizhen Chen
Gang Li
author_sort Lizhen Chen
title Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
title_short Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
title_full Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
title_fullStr Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
title_full_unstemmed Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
title_sort existence results for generalized bagley-torvik type fractional differential inclusions with nonlocal initial conditions
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2018-01-01
description In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.
url http://dx.doi.org/10.1155/2018/2761321
work_keys_str_mv AT lizhenchen existenceresultsforgeneralizedbagleytorviktypefractionaldifferentialinclusionswithnonlocalinitialconditions
AT gangli existenceresultsforgeneralizedbagleytorviktypefractionaldifferentialinclusionswithnonlocalinitialconditions
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