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.


34M99 Ordinary differential equations in the complex domain
34A08 Fractional ordinary differential equations
34D99 Stability theory for ordinary differential equations
Full Text: DOI


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