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Ulam stability for fractional differential equation in complex domain. (English) Zbl 1239.34106
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.

MSC:
34M99 Ordinary differential equations in the complex domain
34A08 Fractional ordinary differential equations and fractional differential inclusions
34D99 Stability theory for ordinary differential equations
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