Monotone Iterative Technique for Nonlocal Impulsive Finite Delay Differential Equations of Fractional Order
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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.
KeywordsImpulsive fractional differential equations Finite delay Semigroup theory Monotone iterative technique Lower and upper solutions Kuratowskii measure of noncompactness
Mathematics Subject Classification34A08 34G20 34K30 93B05
The authors would like to thank the referees for their valuable comments and suggestions which improved the quality of the manuscript. Kamal Jeet would like to acknowledge DST-SERB, India for carrying out this research work under the research project PDF/2016/003875.
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