Acta Applicandae Mathematicae

, Volume 109, Issue 2, pp 495–505 | Cite as

Unbounded Solutions for a Fractional Boundary Value Problems on the Infinite Interval

Article

Abstract

In this paper, we consider the fractional boundary value problem
$$\left\{\begin{array}{l}\displaystyle D^{a}_{0+}u(t)+f(t,u(t))=0,\quad t\in(0,\infty),~\alpha\in (1,2),\\[2mm]\displaystyle u(0)=0,\quad\lim_{t\rightarrow\infty}D^{a-1}_{0+}u(t)=\beta u(\xi),\end{array}\right.$$
where D 0+ a is the standard Riemann-Liouville fractional derivative. By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem. The fractional modeling is a generalization of the classical integer-order differential equations and it is a very important tool for modeling the anomalous dynamics of numerous processes involving complex systems found in many diverse fields of science and engineering.

Keywords

Boundary value problems Unbounded solution Riemann-Liouville fractional derivative Infinite interval 

Mathematics Subject Classification (2000)

39A60 34B18 34B40 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Mechanics, School of Applied ScienceUniversity of Science and Technology BeijingBeijingChina
  2. 2.Department of MathematicsBeijing Institute of TechnologyBeijingPeople’s Republic of China

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