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

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 measur...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 13
Main Authors Arab, Reza, Nashine, Hemant Kumar, Can, N. H., Binh, Tran Thanh
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 07.01.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Banach spaces
Difference and Functional Equations
Fixed point
Fixed points (mathematics)
Functional Analysis
Functional-integral equation
Integral equations
Mathematics
Mathematics and Statistics
Measure of noncompactness
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Functional-integral equation
47H10
Measure of noncompactness
35K90
Fixed point
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2487-4