$On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses$

On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses

Abstract In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations a...

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Main Authors:	Bo Zhu, Baoyan Han, Lishan Liu, Wenguang Yu
Format:	Article
Language:	English
Published:	SpringerOpen 2020-09-01
Series:	Boundary Value Problems
Subjects:	Nonlinear fractional partial integro-differential equations of mixed type Non-instantaneous impulses α-order solution operator General Banach contraction mapping principle Krasnoselskii’s fixed point theorem
Online Access:	http://link.springer.com/article/10.1186/s13661-020-01451-z

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spelling	doaj-484d916319464020a33473c9c8c899342020-11-25T03:31:15ZengSpringerOpenBoundary Value Problems1687-27702020-09-012020111210.1186/s13661-020-01451-zOn the fractional partial integro-differential equations of mixed type with non-instantaneous impulsesBo Zhu0Baoyan Han1Lishan Liu2Wenguang Yu3School of Mathematics and Quantitative Economics, Shandong University of Finance and EconomicsCommon Course Teaching Department, Shandong University of Art and DesignSchool of Mathematical Sciences, Qufu Normal UniversitySchool of Insurance, Shandong University of Finance and EconomicsAbstract In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order solution operator.http://link.springer.com/article/10.1186/s13661-020-01451-zNonlinear fractional partial integro-differential equations of mixed typeNon-instantaneous impulsesα-order solution operatorGeneral Banach contraction mapping principleKrasnoselskii’s fixed point theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bo Zhu Baoyan Han Lishan Liu Wenguang Yu
spellingShingle	Bo Zhu Baoyan Han Lishan Liu Wenguang Yu On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses Boundary Value Problems Nonlinear fractional partial integro-differential equations of mixed type Non-instantaneous impulses α-order solution operator General Banach contraction mapping principle Krasnoselskii’s fixed point theorem
author_facet	Bo Zhu Baoyan Han Lishan Liu Wenguang Yu
author_sort	Bo Zhu
title	On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
title_short	On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
title_full	On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
title_fullStr	On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
title_full_unstemmed	On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
title_sort	on the fractional partial integro-differential equations of mixed type with non-instantaneous impulses
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2770
publishDate	2020-09-01
description	Abstract In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order solution operator.
topic	Nonlinear fractional partial integro-differential equations of mixed type Non-instantaneous impulses α-order solution operator General Banach contraction mapping principle Krasnoselskii’s fixed point theorem
url	http://link.springer.com/article/10.1186/s13661-020-01451-z
work_keys_str_mv	AT bozhu onthefractionalpartialintegrodifferentialequationsofmixedtypewithnoninstantaneousimpulses AT baoyanhan onthefractionalpartialintegrodifferentialequationsofmixedtypewithnoninstantaneousimpulses AT lishanliu onthefractionalpartialintegrodifferentialequationsofmixedtypewithnoninstantaneousimpulses AT wenguangyu onthefractionalpartialintegrodifferentialequationsofmixedtypewithnoninstantaneousimpulses
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On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses

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