Abstract and Applied Analysis
Volume 2010 (2010), Article ID 865139, 8 pages
doi:10.1155/2010/865139
Research Article

Asymptotically Linear Solutions for Some Linear Fractional Differential Equations

Dumitru Băleanu,1 Octavian G. Mustafa,2 and Ravi P. Agarwal3

1Department of Mathematics & Computer Science, Çankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, Turkey
2Department of Mathematics & Computer Science, University of Craiova, DAL, Tudor Vladimirescu 26, 200534 Craiova, Romania
3Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

Received 19 September 2010; Accepted 9 November 2010

Academic Editor: Paul Eloe

Copyright © 2010 Dumitru Băleanu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish here that under some simple restrictions on the functional coefficient 𝑎 ( 𝑡 ) the fractional differential equation 0 𝐷 𝛼 𝑡 [ 𝑡 𝑥 − 𝑥 + 𝑥 ( 0 ) ] + 𝑎 ( 𝑡 ) 𝑥 = 0 , 𝑡 > 0 , has a solution expressible as 𝑐 𝑡 + 𝑑 + 𝑜 ( 1 ) for 𝑡 → + ∞ , where 0 𝐷 𝛼 𝑡 designates the Riemann-Liouville derivative of order 𝛼 ∈ ( 0 , 1 ) and 𝑐 , 𝑑 ∈ ℝ .