Solvability of functional-integral equations (fractional order) using measure of noncompactness

Solvability of functional-integral equations (fractional order) using measure of noncompactness

Abstract We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrar...

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Main Authors: Reza Arab, Hemant Kumar Nashine, N. H. Can, Tran Thanh Binh
Format: Article
Language:English
Published: SpringerOpen 2020-01-01
Series:Advances in Difference Equations
Subjects:
Fixed point
Measure of noncompactness
Functional-integral equation
Online Access:https://doi.org/10.1186/s13662-019-2487-4
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spelling doaj-51951e0cee9b4022a7dbdf681321ed702021-01-10T12:52:18ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111310.1186/s13662-019-2487-4Solvability of functional-integral equations (fractional order) using measure of noncompactnessReza Arab0Hemant Kumar Nashine1N. H. Can2Tran Thanh Binh3Department of Mathematics, Sari Branch, Islamic Azad UniversityDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyApplied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang UniversityInstitute of Research and Development, Duy Tan UniversityAbstract We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.https://doi.org/10.1186/s13662-019-2487-4Fixed pointMeasure of noncompactnessFunctional-integral equation
collection DOAJ
language English
format Article
sources DOAJ
author Reza Arab
Hemant Kumar Nashine
N. H. Can
Tran Thanh Binh
spellingShingle Reza Arab
Hemant Kumar Nashine
N. H. Can
Tran Thanh Binh
Solvability of functional-integral equations (fractional order) using measure of noncompactness
Advances in Difference Equations
Fixed point
Measure of noncompactness
Functional-integral equation
author_facet Reza Arab
Hemant Kumar Nashine
N. H. Can
Tran Thanh Binh
author_sort Reza Arab
title Solvability of functional-integral equations (fractional order) using measure of noncompactness
title_short Solvability of functional-integral equations (fractional order) using measure of noncompactness
title_full Solvability of functional-integral equations (fractional order) using measure of noncompactness
title_fullStr Solvability of functional-integral equations (fractional order) using measure of noncompactness
title_full_unstemmed Solvability of functional-integral equations (fractional order) using measure of noncompactness
title_sort solvability of functional-integral equations (fractional order) using measure of noncompactness
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2020-01-01
description Abstract We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.
topic Fixed point
Measure of noncompactness
Functional-integral equation
url https://doi.org/10.1186/s13662-019-2487-4
work_keys_str_mv AT rezaarab solvabilityoffunctionalintegralequationsfractionalorderusingmeasureofnoncompactness
AT hemantkumarnashine solvabilityoffunctionalintegralequationsfractionalorderusingmeasureofnoncompactness
AT nhcan solvabilityoffunctionalintegralequationsfractionalorderusingmeasureofnoncompactness
AT tranthanhbinh solvabilityoffunctionalintegralequationsfractionalorderusingmeasureofnoncompactness
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