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      Existence theory for nonlocal boundary value problems involving mixed fractional derivatives

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      Nonlinear Analysis: Modelling and Control

      Vilnius University Press

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          Abstract

          In this paper, we develop the existence theory for a new kind of nonlocal three-point boundary value problems for differential equations and inclusions involving both left Caputo and right Riemann–Liouville fractional derivatives. The Banach and Krasnoselskii fixed point theorems and the Leray–Schauder nonlinear alternative are used to obtain the desired results for the singlevalued problem. The existence of solutions for the multivalued problem concerning the upper semicontinuous and Lipschitz cases is proved by applying nonlinear alternative for Kakutani maps and Covitz and Nadler fixed point theorem. Examples illustrating the main results are also presented.

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          Author and article information

          Journal
          Nonlinear Analysis: Modelling and Control
          NAMC
          Vilnius University Press
          2335-8963
          1392-5113
          November 15 2019
          November 07 2019
          : 24
          : 6
          Article
          10.15388/NA.2019.6.6
          © 2019

          All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.

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