Existence for boundary value problems of two-term Caputo fractional differential equations

Volume 10, Issue 2, pp 511--520 http://dx.doi.org/10.22436/jnsa.010.02.16

Publication Date: February 20, 2017 Submission Date: November 02, 2016

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Authors

Badawi Hamza Elbadawi Ibrahim - School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China. Qixiang Dong - School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China. Zhenbin Fan - School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China.

Abstract

This paper is concerned with a class of boundary value problem of nonlinear fractional differential equation \(^cD^\alpha u(t)-a^cD^\beta u(t)+f(t,u(t))=0\). This equation may be regarded as an extension of Bagley-Torvik equations. Some new existence and uniqueness results are obtained by using standard Banach contraction principle and Krasnoselskii’s fixed point theorem.

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Keywords

• Fractional derivative
• differential equation
• boundary value problem.

MSC

•  34A08

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