Existence and viability for fractional differential equations with initial conditions at inner points

Volume 9, Issue 5, pp 2590--2603 http://dx.doi.org/10.22436/jnsa.009.05.56

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Authors

Qixiang Dong - School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China.

Abstract

This paper is concerned with nonlinear fractional differential equations with the Caputo derivative. Existence results are obtained for terminal value problems and initial value problems with initial conditions at inner points. It is also proved that the sufficient condition in order that a locally closed subset be a viable domain is the tangency condition. As a corollary, the existence of positive solutions is obtained.

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Keywords

• Fractional derivative
• differential equation
• initial value problem
• viability
• tangency condition.

MSC

•  34A08
•  35F25
•  45M99

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