Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation

Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (2): 293-300.

Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation

1. School of Mathematics, Jiaying University 2. School of Mathematical Science, South China Normal University

Received:2010-12-03 Online:2012-06-30 Published:2023-03-31
About author:SONG Li-mei(1975-), female, native of Meizhou, Guangdong, a lecturer of Jiaying University, engages in ordinary diﬀerential equations.
Supported by:
Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)； Supported by the NSF of Guangdong Province(10151063101000003)

Abstract

Abstract: In this paper, we study a Dirichlet-type boundary value problem (BVP) of nonlinear fractional differential equation with an order α∈(3,4], where the fractional derivative D^α_o+ is the standard Riemann-Liouville fractional derivative. By constructing the Green function and investigating its properties, we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP. The Krasnosel’skii fixed-point theorem in cones is used here. We also give an example to illustrate the applicability of our results.

Key words: fractional differential equation, boundary value problem, positive solution; fractional Green function, fixed-point theorem in cones

CLC Number:

O175.8

SONG Li-mei, WENG Pei-xuan. Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 293-300.

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Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Diﬀerential Equation

1. School of Mathematics, Jiaying University 2. School of Mathematical Science, South China Normal University

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