International Journal of Differential Equations

Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

Cheng-Min Su, Jian-Ping Sun, and Ya-Hong Zhao

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Abstract

In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: D 0 + q C u t = f t , u t ,   t 0,1 , u 0 = u 0 = 0 , D 0 + σ 1 C u 1 = λ I 0 + σ 2 u 1 , where 2 < q < 3 , 0 < σ 1 1 , σ 2 > 0 , and λ Γ 2 + σ 2 / Γ 2 - σ 1 . The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

Article information

Source
Int. J. Differ. Equ., Volume 2017 (2017), Article ID 4683581, 7 pages.

Dates
Received: 11 October 2016
Revised: 14 December 2016
Accepted: 15 December 2016
First available in Project Euclid: 24 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1487905255

Digital Object Identifier
doi:10.1155/2017/4683581

Mathematical Reviews number (MathSciNet)
MR3607978

Zentralblatt MATH identifier
06915935

Citation

Su, Cheng-Min; Sun, Jian-Ping; Zhao, Ya-Hong. Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation. Int. J. Differ. Equ. 2017 (2017), Article ID 4683581, 7 pages. doi:10.1155/2017/4683581. https://projecteuclid.org/euclid.ijde/1487905255


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