Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative

Mouffak Benchohra, Jamal E. Lazreg

Abstract


The purpose of this paper is to establish some  types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit Hadamard fractional-order differential equation.

Keywords


Initial value problem, Hadamard's fractional derivative, implicit fractional differential equations, fractional integral, existence, Gronwall's lemma, fixed point, Ulam-Hyers stability, Ulam-Hyers-Rassias stability.

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DOI: http://dx.doi.org/10.24193/subbmath.2017.0003

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