Banach space

Fixed-point theorem

Functional differential equation

Functional equation

Differential equation

Applied mathematics

Stability (learning theory)

Computer science

Thermodynamics

Physics

Mathematics

Differential (mechanical device)

Exponential function

Mathematical analysis

Fractional calculus

Machine learning

AIMS Mathematics

From the first results on Ulam-Hyers stability, what has been noted is the exponential growth of the researchers dedicated to investigating Ulam-Hyers stability of fractional differential equation solutions whether they are functional, evolution, impulsive, among others. However, some issues and problems still need to be addressed. An intensifying problem is the small amount of work on Ulam-Hyers stability of solutions of fractional functional differential equations through more general fractional operators. In this sense, in this paper, we present a study on the Ulam-Hyers and UlamHyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.

Ulam-Hyers stabilities of fractional functional differential equations