Ulam Stability for Fractional Differential Equation in Complex Domain

Abstract

The present paper deles with a fractional differential equation $z^{\alpha }{D}_z^{\alpha }u\left(z\right)+zu\text{'}\left(z\right)+(z^2-a^2)u\left(z\right)={\sum }_{n=0}^{\infty }{a}_n{z}^{n+\alpha }$, , where 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.