Existence and Stability of Solutions to Differential Equations via the Deformable Derivative and Laplace Transform

Abstract

In this short note, we establish the Existence and stability of solutions of an abstract semilinear differential equation governed by the so-called deformable derivative. We achieve our results using Banach’s contraction principle, the Laplace transform, and the Gronwall inequality. These results are new in the context of fractional differential equations.