The paper is devoted to investigating a Cauchy problem governed by nonclassical heat equation with involution. The problem is severely ill‐posed in the sense of Hadamard by violating the continuous dependence upon the input Cauchy data. Therefore, in order to obtain a stable solution, we shall use a modified Pseudo‐Parabolic Regularization Method. The main idea is to add a correction term by introducing a third‐order derivation operator to formulate a sequence of well‐posed problems that depend on a regularization parameter ε. Further, we show that the approximate problems are well posed, and we prove some convergence results.

A preconditioning version of the Kozlov–Maz’ya iteration method for the stable identification of missing boundary data is presented for an ill-posed problem governed by generalized elliptic equations. The ill-posed data identification problem is reformulated as a sequence of well-posed fractional elliptic equations in infinite domain. Moreover, some convergence results are established. Finally, numerical results are included showing the accuracy and efficiency of the proposed method.