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Existence and Controllability for Nonlinear Fractional Differential Inclusions with Nonlocal Boundary Conditions And Time-Varying Delay.

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Abstract

This paper discusses the existence and controllability of a class of fractional order evolution inclusions with time-varying delay. In the weak topology setting we establish the existence of solutions. Then the controllability of this system with a nonlocal condition is established by applying the Glicksberg-Ky Fan fixed point theorem. As an application, nonlocal problems of a fractional reaction-diffusion equation with a discontinuous nonlinear term is examined.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Bohai University, Jinzhou, Liaoning, 121013, China

    Yi Cheng

  2. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA

    Ravi P. Agarwal

  3. Department of Mathematics, Faculty of Science King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Ravi P. Agarwal

  4. School of Mathematics, Statistics and Applied Mathematics National University of Ireland, Galway, Ireland

    Donal O’ Regan

Authors
  1. Yi Cheng
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  2. Ravi P. Agarwal
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  3. Donal O’ Regan
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Correspondence to Yi Cheng.

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Cheng, Y., Agarwal, R.P. & Regan, D.O. Existence and Controllability for Nonlinear Fractional Differential Inclusions with Nonlocal Boundary Conditions And Time-Varying Delay.. FCAA 21, 960–980 (2018). https://doi.org/10.1515/fca-2018-0053

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