Existence of solutions for a singular system of nonlinear fractional differential equations

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• 作者：Wenquan Feng^a ; ^{fengwenquan522@163.com"" rel=""nofollow} ; Shurong Sun^a ; ^b ; ^{sshrong@163.com"" rel=""nofollow} ; Zhenlai Han^a ; ^c ; ^{hanzhenlai@163.com"" rel=""nofollow} ; Yige Zhao^a ; ^{zhaoeager@126.com"" rel=""nofollow}
• 关键词：Fractional order ; Singular system ; Fixed point theorem ; Fractional Green’ ; s function
• 刊名：Computers and Mathematics with Applications
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：62
• 期：3
• 页码：1370-1378
• 全文大小：250 K

文摘

In this paper, we establish the existence of positive solutions for a singular system of nonlinear fractional differential equations. The differential operator is taken in the standard Riemann–Liouville sense. By using Green’s function and its corresponding properties, we transform the derivative systems into equivalent integral systems. The existence is based on a nonlinear alternative of Leray–Schauder type and Krasnoselskii’s fixed point theorem in a cone.