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Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem

Zahra Ahmadi, Rahmatollah Lashkaripour ORCID logo, Hamid Baghani and Shapour Heidarkhani


In this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders γ ( n 1 1 , n 1 ] and η ( n 2 1 , n 2 ] for any n 1 , n 2 . We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.

Corresponding author: Shapour Heidarkhani, Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran, E-mail:

  1. Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.


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Received: 2019-11-02
Accepted: 2020-10-16
Published Online: 2020-11-09
Published in Print: 2021-10-26

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