Acta Applicandae Mathematicae

, Volume 109, Issue 2, pp 495–505

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

Article

DOI: 10.1007/s10440-008-9329-9

Cite this article as:
Zhao, X. & Ge, W. Acta Appl Math (2010) 109: 495. doi:10.1007/s10440-008-9329-9

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 D0+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 problemsUnbounded solutionRiemann-Liouville fractional derivativeInfinite interval

Mathematics Subject Classification (2000)

39A6034B1834B40

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