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Kucche, Kishor D.; Sutar, Sagar T.

On existence and stability results for nonlinear fractional delay differential equations. (English) Zbl 1424.34270

Bol. Soc. Parana. Mat. (3) 36, No. 4, 55-75 (2018).
Summary: We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, generalized Ulam-Hyers-Rassias stability, \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability and generalized \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability of fractional order delay differential equations.

Cited in 18 Documents

MSC:

34K37 Functional-differential equations with fractional derivatives
34K27 Perturbations of functional-differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

fractional delay differential equation; fixed point theorem; existence and uniqueness; successive approximation; Ulam-Hyers stability; \(\mathbb{E}_{\alpha}\)-Ulam-Hyers stability
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References:

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