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Mathematical Communications, Vol. 17 No. 2, 2012.

Original scientific paper

Differential equations of fractional order $\alpha\in (2,3)$ with boundary value conditions in abstract Banach spaces

JinRong Wang ; Department of Mathematics, Guizhou University, Guiyang, Guizhou, P. R. China
Linli Lv ; Department of Mathematics, Guizhou University, Guiyang, Guizhou, P. R. China
Wei Wei ; Department of Mathematics, Guizhou University, Guiyang, Guizhou, P. R. China

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page 371-387

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Abstract

In this paper, we study boundary value problems for differential
equations involving Caputo derivative of order $\alpha\in (2,3)$ in
Banach spaces. Some sufficient conditions for the existence and
uniqueness of solutions are established by virtue of fractional
calculus, a special singular type Gronwall inequality and fixed
point method under some suitable conditions. Examples are given to
illustrate the main results.

Keywords

fractional order derivative; differential equations; boundary value problems; existence and uniqueness; fixed point method

Hrčak ID:

93235

URI

https://hrcak.srce.hr/93235

Publication date:

5.12.2012.

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