Stability (learning theory)

Physics

Nonlinear system

Uniqueness

Mathematics

Laplace transform

Machine learning

Fractional calculus

Mathematical analysis

Picard–Lindelöf theorem

Banach fixed-point theorem

Gronwall's inequality

Computer science

Inequality

Fixed point

Quantum mechanics

Differential equation

Applied mathematics

Fixed-point theorem

In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo–Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer’s fixed point theorem. Finally, two examples are given to illustrate our main results.

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative