Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel

A study on fractional differential equations using the fractional Fourier transform

“…As a result, the development of stability of nonlinear FODE is a bit slow. Recently, Liu et al [37] discussed the stability of the following FODE:…”

Riemann-Stieltjes Integral boundary value problems involving mixed Riemann-Liouville and Caputo fractional derivatives

“…Fractional-order boundary value problems have recently been studied by many researchers. One can find a variety of results for such problems involving different kinds of fractional differential equations and boundary conditions in [10]- [22] and the references cited therein.…”

A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations

“…In 1978, Rassias [2] introduced a new definition of generalized Hyers-Ulam stability by the constant ε by a variable, and obtained the stability of Hyers-Ulam-Rassias for functional equation. There is a rich literature on this topic for standard integer-order equations (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). In addition, the same stability concepts are introduced to find approximate solutions to fractional differential equations, see [18,19] and the references therein.…”