Abstract and Applied Analysis
Volume 2012 (2012), Article ID 649517, 8 pages
http://dx.doi.org/10.1155/2012/649517
Research Article

Ulam Stability for Fractional Differential Equation in Complex Domain

Rabha W. Ibrahim

Institute of Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, Malaysia

Received 3 October 2011; Accepted 22 November 2011

Academic Editor: Norio Yoshida

Copyright © 2012 Rabha W. Ibrahim. 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

The present paper deles with a fractional differential equation 𝑧 𝛼 𝐷 𝛼 𝑧 𝑢 ( 𝑧 ) + 𝑧 𝑢 ′ ( 𝑧 ) + ( 𝑧 2 − 𝑎 2 ∑ ) 𝑢 ( 𝑧 ) = ∞ 𝑛 = 0 𝑎 𝑛 𝑧 𝑛 + 𝛼 , 1 < 𝛼 ≤ 2 , where 𝑧 ∈ 𝑈 ∶ = { 𝑧 ∶ | 𝑧 | < 1 } in sense of Srivastava-Owa fractional operators. The existence and uniqueness of holomorphic solutions are established. Ulam stability for the approximation and holomorphic solutions are suggested.