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In this paper we study the Hyers-Ulam-Rassias stability of Cauchy equation in Felbin's type fuzzy normed linear spaces. As a result we give an example of a fuzzy normed linear space such that the fuzzy version of the stability problem remains true, while it fails to be correct in classical analysis.This shows how the category of fuzzy normed linear spaces differs from the classical normed linear spaces in general.

In this paper, we investigate the solutions of a class of-Hilfer fractional differential equations with the initial values in the sense of-fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented.

‎In this paper‎, ‎for a singular perturbation problem consist of the Cauchy-Euler equation with local and non-local boundary conditions‎. ‎We investigate the condition of the self-adjoint and the non-self-adjoint‎, ‎also look for the formation or non-formation of boundary layers for local boundary conditions using the Frequent uniform limit method‎. ‎Also‎, ‎for the state of non-local conditions‎, ‎we convert the non-local boundary conditions into local conditions by finding the fundamental solution and then obtaining the necessary conditions with the help of the 4-step method‎. ‎Finally‎, ‎we determine the formation or non-formation of a boundary layer for non-local conditions such as local conditions‎.

A new simplified analytical formula is given for solving the Cauchy problem for a homogeneous system of fractional order linear differential equations with constant coefficients (SFOLDECC). The matrix exponential function in this formula is re-placed by a Taylor series. Next, an analytical expression of the integral is obtained, with the help of which, for the transition matrix, a relation is obtained that allows one to obtain a solution of the Cauchy problem with high accuracy. The results also apply to the case of inhomogeneous systems with constant perturbations and are illustrated by numerical examples.