$Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions$

Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions

Abstract This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our...

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Main Authors:	Mohamed A. E. Herzallah, Ashraf H. A. Radwan
Format:	Article
Language:	English
Published:	SpringerOpen 2019-11-01
Series:	Journal of the Egyptian Mathematical Society
Subjects:	Caputo derivative Differential inclusion Nonlocal conditions Deviated-advanced nonlocal condition Schauder’s fixed point theorem
Online Access:	http://link.springer.com/article/10.1186/s42787-019-0048-3

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spelling	doaj-871cca3251074be6816419d7405efe932020-11-25T04:07:57ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282019-11-0127111510.1186/s42787-019-0048-3Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditionsMohamed A. E. Herzallah0Ashraf H. A. Radwan1Faculty of Science, Zagazig UniversityFaculty of Science, Zagazig UniversityAbstract This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our results will be accomplished by using the nonlinear Leray-Schauder’s alternative fixed point theorem. The main results are well illustrated with the aid of an example.http://link.springer.com/article/10.1186/s42787-019-0048-3Caputo derivativeDifferential inclusionNonlocal conditionsDeviated-advanced nonlocal conditionSchauder’s fixed point theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohamed A. E. Herzallah Ashraf H. A. Radwan
spellingShingle	Mohamed A. E. Herzallah Ashraf H. A. Radwan Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions Journal of the Egyptian Mathematical Society Caputo derivative Differential inclusion Nonlocal conditions Deviated-advanced nonlocal condition Schauder’s fixed point theorem
author_facet	Mohamed A. E. Herzallah Ashraf H. A. Radwan
author_sort	Mohamed A. E. Herzallah
title	Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
title_short	Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
title_full	Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
title_fullStr	Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
title_full_unstemmed	Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
title_sort	existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions
publisher	SpringerOpen
series	Journal of the Egyptian Mathematical Society
issn	2090-9128
publishDate	2019-11-01
description	Abstract This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our results will be accomplished by using the nonlinear Leray-Schauder’s alternative fixed point theorem. The main results are well illustrated with the aid of an example.
topic	Caputo derivative Differential inclusion Nonlocal conditions Deviated-advanced nonlocal condition Schauder’s fixed point theorem
url	http://link.springer.com/article/10.1186/s42787-019-0048-3
work_keys_str_mv	AT mohamedaeherzallah existenceofmildsolutionstosemilinearfractionaldifferentialinclusionwithdeviatedadvancednonlocalconditions AT ashrafharadwan existenceofmildsolutionstosemilinearfractionaldifferentialinclusionwithdeviatedadvancednonlocalconditions
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Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions

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