Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators-Reference-Cited by-同舟云学术

Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators

Published:2020-02-01 Issue:1 Volume:23 Page:268-291
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Chen Pengyu¹,Zhang Xuping¹,Li Yongxiang¹

Affiliation:

1. Department of Mathematics , Northwest Normal University , Lanzhou , 730070 , People’s Republic of China

Abstract

Abstract In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder’s fixed point theorem as well as the theory of α-order solution operator and α-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0011/pdf

Reference51 articles.

1. N. Abada, M. Benchohra, H. Hammouche, Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions. J. Differential Equations246, No 10 (2009), 3834–3863.

2. R.P. Agarwal, V. Lakshmikantham, J.J. Nieto, On the concept of solutions for fractional differential equations with uncertainly. Nonlinear Anal. 72, No 6 (2010), 2859–2862.

3. D. Araya, C. Lizama, Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal. 69, No 11 (2008), 3692–3705.

4. E.G. Bajlekova, Fractional Evolution Equations in Banach Spaces. PhD Thesis, Department of Mathematics, Eindhoven University of Technology (2001).

5. A. Boucherif, Semilinear evolution inclutions with nonlocal conditions. Appl. Math. Letters22, No 8 (2009), 1145–1149.

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