An investigation on the existence, uniqueness and Ulam-Hyers stability of solution for a fractional differential problem

Abstract: In this seminar, we will analyse a fractional differential problem in terms of existence, uniqueness and stability of its solution. Specifically, we will consider an initial value problem with a Riemann-Liouville fractional derivative. Using some techniques of Functional Analysis, as the fixed point theory, and some integral inequalities, we will obtain sufficient conditions that guarantee that the solutions of the problem exist and sufficient conditions for its uniqueness. We also obtain a stability result by Ulam-Hyers and Ulam-Hyers-Rassias.