The paper defines a delayed Mittag-Leffler function, derives explicit solutions for linear nonhomogeneous fractional delay Langevin equations, proves existence/uniqueness via fixed-point arguments, and establishes Ulam-Hyers stability.
From dynamical systems to the langevin eq uation
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Delayed Langevin type equations with two fractional derivatives
The paper defines a delayed Mittag-Leffler function, derives explicit solutions for linear nonhomogeneous fractional delay Langevin equations, proves existence/uniqueness via fixed-point arguments, and establishes Ulam-Hyers stability.