Ulam stability for fractional differential equation in complex domain (Q410210)

Summary: The present paper deals with a fractional differential equation \[ z^\alpha D^\alpha_z u(z) + zu'(z) + (z^2 - a^2)u(z) = \sum^\infty_{n=0} a_nz^{n+\alpha}, \] \(1 < \alpha \leq 2\), where \(z \in U : = \{z : |z| < 1\}\) 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.