Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem-Reference-Cited by-同舟云学术

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

Published:2020-11-09 Issue:6 Volume:22 Page:797-807
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Ahmadi Zahra¹,Lashkaripour Rahmatollah¹^ORCID,Baghani Hamid¹,Heidarkhani Shapour²

Affiliation:

1. Department of Mathematics , Faculty of Mathematics, University of Sistan and Baluchestan , Zahedan , Iran

2. Department of Mathematics , Faculty of Sciences, Razi University , Kermanshah , Iran

Abstract

Abstract 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 ]

$\gamma \in \left({n}_{1}-1,{n}_{1}\right]$

and η ∈ ( n 2 − 1 , n 2 ]

$\eta \in \left({n}_{2}-1,{n}_{2}\right]$

for any n 1 , n 2 ∈ ℕ

${n}_{1},{n}_{2}\in \mathrm{ℕ}$

. 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2019-0273/pdf

Reference28 articles.

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