Existence of positive solutions for nonlinear fractional functional differential equation

Authors:
Yulin Zhao;Haibo Chen;Li Huang
Affiliations:
School of Science, Hunan University of Technology, Zhuzhou, 412008, PR China;Department of Mathematics, Central South University, Changsha, 410075, PR China;School of Science, Hunan University of Technology, Zhuzhou, 412008, PR China
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 3
Cited 0

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Multiple solutions for fractional differential equations with nonlinear boundary conditions

Computers & Mathematics with Applications
The existence of multiple positive solutions for singular functional differential equations with sign-changing nonlinearity

Journal of Computational and Applied Mathematics

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Abstract

In this paper, the existence of positive solutions for the nonlinear Caputo fractional functional differential equation in the form {D"0"+^qy(t)+r(t)f(y"t)=0,@?t@?(0,1),q@?(n-1,n],y^(^i^)(0)=0,0@?i@?n-3,@ay^(^n^-^2^)(t)-@by^(^n^-^1^)(t)=@h(t),t@?[-@t,0],@cy^(^n^-^2^)(t)+@dy^(^n^-^1^)(t)=@x(t),t@?[1,1+a] is studied. By constructing a special cone and using Krasnosel'skii's fixed point theorem, various results on the existence of at least one or two positive solutions to the fractional functional differential equation are established. The main results improve and generalize the existing results.