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

By Kui Liu, Michal Feckan, Donal O'Regan, Jinrong Wang. Mathematics, 2019

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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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/51c7db2e31d0f345de43f6e80c67227d4f0c752d