On the Ulam–Hyers stability of first order differential systems with nonlocal initial conditions

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].…”

Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative

“…In the theory of functional equations, there is some special kind of data dependence [3,13,17,20]. For the advanced contribution on Ulam stability for FDEs, we refer the reader to [12,23,25,26].…”

Dynamics and stability of Hilfer-Hadamard type fractional pantograph equations with boundary conditions

“…There are some works on FDEs with Hadamard fractional derivative, even if it has been studied many years ago (see for example [2,7,8]). Motivation and basic theoretical development for the research related to Ulam-Hyers stability and Ulam-Hyers-Rassias stability problems to various forms of ordinary differential and integral equations of integer orders can be found in [5,14,16,19]. We mention here few recent on Ulam stabilities by different researchers [1,14,21,29,30,31,32]; also see the references cited therein.…”