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2013•Abstract and Applied AnalysisOpen access

The Solvability and Optimal Controls for Some Fractional Impulsive Equation

Xianghu Liu, Zhenhai Liu, Jiangfeng Han

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Abstract

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

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What this paper is about

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

Key concepts: Mathematics, Uniqueness, Fixed-point theorem, Fractional calculus, Gronwall's inequality, Applied mathematics, Schauder fixed point theorem, Mathematical analysis

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