Ulam-Hyers-Rassias stability of pseudoparabolic partial differential equations

Abstract

The aim of this paper is to give some types of Ulam stability for a pseudoparabolic partial differential equation. In this case we consider Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. We investigate some new applications of the Gronwall lemmas to the Ulam stability of a nonlinear pseudoparabolic partial differential equations.

Stability Results for the Darboux Problem of Conformable Partial Differential Equations

“…The monographs [12,13] present a comprehensive overview of the UHS and UHRS of various functional equations. Recently, the study of Ulam's problem has been extended to include a wide range of functional equations, such as symmetrical differential equations, integral equations, integro-differential equations, partial differential equations, and other types of equations (see [8,[14][15][16][17][18][19][20][21][22]). For example, in [15], the authors studied the UHRS of pseudoparabolic partial differential equations, while in [19], the UHS of pantograph fractional stochastic differential equations was investigated.…”

Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

“…Rassias in [15]. Ulam-Hyers stability of partial differential equations was also studied in [16][17][18][19][20][21]. In [22], Brzdek, Popa, Rasa and Xu presented a unified and systematic approach to the field.…”

Semi-Hyers–Ulam–Rassias Stability of the Convection Partial Differential Equation via Laplace Transform

“…Rassias. The Ulam-Hyers stability of partial differential equations was also studied in [21][22][23][24][25][26].…”