Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation

Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation

In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check th...

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Main Authors: Mian Bahadur Zada, Muhammad Sarwar, Thabet Abdeljawad, Fahd Jarad
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/4581035
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spelling doaj-f7ea1cf74bd14f57860d6e16281b8d092020-11-30T09:11:27ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/45810354581035Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential EquationMian Bahadur Zada0Muhammad Sarwar1Thabet Abdeljawad2Fahd Jarad3Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhw, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhw, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, TurkeyIn this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given.http://dx.doi.org/10.1155/2020/4581035
collection DOAJ
language English
format Article
sources DOAJ
author Mian Bahadur Zada
Muhammad Sarwar
Thabet Abdeljawad
Fahd Jarad
spellingShingle Mian Bahadur Zada
Muhammad Sarwar
Thabet Abdeljawad
Fahd Jarad
Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
Journal of Function Spaces
author_facet Mian Bahadur Zada
Muhammad Sarwar
Thabet Abdeljawad
Fahd Jarad
author_sort Mian Bahadur Zada
title Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
title_short Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
title_full Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
title_fullStr Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
title_full_unstemmed Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
title_sort generalized darbo-type f-contraction and f-expansion and its applications to a nonlinear fractional-order differential equation
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given.
url http://dx.doi.org/10.1155/2020/4581035
work_keys_str_mv AT mianbahadurzada generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation
AT muhammadsarwar generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation
AT thabetabdeljawad generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation
AT fahdjarad generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation
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