Laplace transform and Hyers–Ulam stability of linear differential equations

Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

“…More about stability of ordinary differential equations and fractional differential equations can be found in [7], [11], [12] and [13]. Theorem 2.2.…”

“…Recently, by applying Laplace transform method, Rezaei, Jung, and Rassias discussed Hyers-Ulam stability of linear differential equations (see [11]). Popa and Raşa proved the generalized Hyers-Ulam stability of linear differential equations in a Banach space (see [10]).…”

An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order

“…Soon afterwards, such stability results of the differential equation y = λy in various abstract spaces have been obtained by Miura and Takahasi et al [12,13,22]. Since then, many interesting results on the Ulam stability of different types of differential equations have been established by various authors [1,3,4,5,7,8,9,10,11,14,15,17,18,19,20,21,23].…”

Hyers-Ulam Stability of Third Order Euler’s Differential Equations

“…In 1940, Ulam gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems [1]. Among such problems is a problem concerning the stability of functional equations: give conditions in order for a linear function near an approximately linear function to exist.…”