On generalized Hyers-Ulam stability of admissible functions. (English) Zbl 1237.39033

Summary: We consider the Hyers-Ulam stability for the following fractional differential equations in sense of Srivastava-Owa fractional operators (derivative and integral) defined in the unit disk: \(D^\beta_z f(z) = G(f(z)\), \(D^\alpha_z f(z)\), \(zf'(z); z)\), \(0 < \alpha < 1 < \beta \leq 2\), in a complex Banach space. Furthermore, a generalization of the admissible functions in complex Banach spaces is imposed, and applications are illustrated.


39B82 Stability, separation, extension, and related topics for functional equations
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
34A08 Fractional ordinary differential equations
Full Text: DOI


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