Monotone Iterative Technique for Nonlocal Impulsive Finite Delay Differential Equations of Fractional Order

The paper is concerned with the extension of a monotone iterative technique to impulsive finite delay differential equations of fractional order with a nonlocal initial condition in an ordered Banach space. We study the existence of extremal mild solutions with or without assuming the compactness of...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 30; no. 4; pp. 801 - 816
Main Authors Jeet, Kamal, Sukavanam, N., Bahuguna, D.
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.10.2022
Springer Nature B.V
Subjects
Banach spaces
Computer Science
Differential equations
Engineering
Fractional calculus
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Research
Semigroups
34K30
Monotone iterative technique
Kuratowskii measure of noncompactness
34G20
93B05
Impulsive fractional differential equations
Finite delay
Lower and upper solutions
Semigroup theory
34A08
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Summary:The paper is concerned with the extension of a monotone iterative technique to impulsive finite delay differential equations of fractional order with a nonlocal initial condition in an ordered Banach space. We study the existence of extremal mild solutions with or without assuming the compactness of a semigroup and also prove the uniqueness of the mild solution of the system. The results are obtained with the help of fractional calculus, a measure of non-compactness, the semigroup theory and monotone iterative technique. Finally, an example is provided to show the application of our main.
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-019-00498-4