Boundary fractional differential equation in a complex domain
1 Institute of Mathematical Sciences, University Malaya, Kuala Lumpur, 50603, Malaysia
2 Institute of Mathematical Sciences, Kent State University, Burton, OH, 44021-9500, USA
Boundary Value Problems 2014, 2014:66 doi:10.1186/1687-2770-2014-66Published: 24 March 2014
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.