Existence results for boundary value problems of nonlinear fractional differential equations

Authors:
Guoqing Chai
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
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)
Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

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On the global existence of solutions to a class of fractional differential equations

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Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order

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Abstract

In this paper, we consider the existence of solutions for the nonlinear fractional differential equation ^CD"0"+^@au(t)+r^CD"0"+^@a^-^1u(t)=f(t,u(t)),t@?(0,1) with the boundary value conditions u(0)=u(1),u(@x)=@h,@x@?(0,1), where ^CD"0"+^@a and ^CD"0"+^@a^-^1 are the standard Caputo derivative with 10. By using the contraction mapping principle and the Schauder fixed point theorem, some existence results are obtained. In addition, Lemma 2.6 in this paper is a valuable tool in seeking solvability of the fractional differential equations.