Positive solutions for boundary-value problems of nonlinear fractional differential equations

Date

2006-03-21

Authors

Zhang, Shuqin

Journal Title

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Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem Dα0 + u(t) = ƒ(t, u(t)), 0 < t < 1 u(0) + u′(0) = 0, u(1) + u′(1) = 0 where 1 < α ≤ 2 is a real number, and Dα0+ is the Caputo's fractional derivative, and ƒ : [0, 1] x [0, +∞) → [0, +∞) is continuous. By means of a fixed-point theorem on cones, some existence and multiplicity results of positive solutions are obtained.

Description

Keywords

Caputo's fractional derivative, Fractional differential equation, Boundary-value problem, Positive solution, Fractional Green's function, Fixed-point theorem

Citation

Zhang, S. (2006). Positive solutions for boundary-value problems of nonlinear fractional differential equations. <i>Electronic Journal of Differential Equations, 2006</i>(36), pp. 1-12.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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