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Open Access Research

Boundary fractional differential equation in a complex domain

Rabha W Ibrahim1* and Jay M Jahangiri2

Author Affiliations

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

2 Institute of Mathematical Sciences, Kent State University, Burton, OH, 44021-9500, USA

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Boundary Value Problems 2014, 2014:66  doi:10.1186/1687-2770-2014-66

Published: 24 March 2014

Abstract

We discuss univalent solutions of boundary fractional differential equations in a complex domain. The fractional operators are taken in the sense of the Srivastava-Owa calculus in the unit disk. The existence of subsolutions and supersolutions (maximal and minimal) is established. The existence of a unique univalent solution is imposed. Applications are constructed by making use of a transformation formula for fractional derivatives as well as generalized fractional derivatives.