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- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-008-9329-9
- Publisher site
- See Article on Publisher Site
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.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2008